Ka Okosun | Vaal University of Technology (original) (raw)

Papers by Ka Okosun

Research paper thumbnail of Mathematical Analysis of a Social Hierarchy-Structured Model for Malaria Transmission Dynamics

SSRN Electronic Journal, 2021

Research paper thumbnail of Application of Optimal Control to the Epidemiology of Fowl Pox Transmission Dynamics in Poultry

Journal of Mathematics and Statistics, 2012

In this study, we present the mathematical model of the transmission dynamics of fowl pox infecti... more In this study, we present the mathematical model of the transmission dynamics of fowl pox infection in poultry. Approach: It describes the interaction between the susceptible and the infected birds which results in a system of ordinary differential equation. Introducing the control which represents the effort in applying chemoprophylaxis control u 1 and treatment control u 2 in birds with fowl pox, the system becomes a system of ordinary differential equations with control. Results: Our optimal control problem involves that in which the number of birds with latent and active fowl pox infections and the cost of treatment controls u 1 (t) and u 2 (t) were minimized subject to the differential Eq. 5-8. This involves the number of birds with active and latent fowl pox respectively as well as the cost of applying chemoprophylaxis control u 1 and treatment u 2 in birds with fowl pox. Conclusion: Analysing the model using Pontryagin's Maximum Principle and optimality conditions, optimal effort necessary to reduce the transmission rate of fowl pox in the poultry has been determined. Hence, it is possible to reduce to reduce the rate of transmission.

Research paper thumbnail of Stability Analysis and Optimal Control of a Lyme Disease Model with Insecticides Spraying and Vaccination

Journal of Biological Systems

This paper studies an SIS-type Lyme transmission model incorporating insecticides spraying and va... more This paper studies an SIS-type Lyme transmission model incorporating insecticides spraying and vaccination as interventions. We obtain the positivity and boundedness of solutions, calculate the basic reproduction number, and discuss the global stability of disease-free and endemic equilibria when the basic reproduction number [Formula: see text] and [Formula: see text], respectively. We apply Pontryagin’s maximum principle to explore an optimal control strategy to minimize the number of infected ticks and hosts and the cost of using insecticides and vaccination. We design numerical simulations to illustrate the effectiveness of theoretical analysis.

Research paper thumbnail of Numerical Investigation of Thermal Stability in a Reactive Sphere of Variable Thermal Conductivity

Thermal stability in a stockpile of combustible material modelled in a spherical domain is invest... more Thermal stability in a stockpile of combustible material modelled in a spherical domain is investigated in this article. The reactive material of the sphere is considered with temperature dependent thermal conductivity and the sphere is assumed to lose heat to the ambient due to exothermic chemical reaction taking place within it. Also, a one-step finite rate irreversible Arrhenius kinetics is assumed to tackle the complicated chemical reaction taking place in this problem. We apply finite difference method (FDM to solve numerically the differential equation governing the problem. FDM is very essential for spatial derivatives discretization. Heat transfer analysis for variation of kinetic parameters embedded within the system, against temperature, is presented graphically and the results are discussed accordingly.

Research paper thumbnail of Investigating the resurgence of malaria prevalence in South Africa between 2015 and 2018: A scoping review

Background Malaria remains a serious concern in most African countries, causing nearly one millio... more Background Malaria remains a serious concern in most African countries, causing nearly one million deaths globally every year. The review aims to examine the extent and nature of the resurgence of malaria prevalence in South Africa.Method Using the Arksey and O'Malley framework, this scoping review included articles published between the year 2015 and 2018 on the resurgence of malaria prevalence in South Africa. Articles were searched from October 2018 to January 2019 using these electronic databases: CINAHL, Pubmed, Science Direct and SCOPUS. Grey literature from Google Scholar was also hand searched. Key search terms and subject headings such as climate variables; climate changes; climatic factors; malaria resurgence; malaria reoccurrence, and malaria increase over epidemic regions in South Africa were used to identify relevant articles. Articles for selection and characterization were performed by three independent reviewers. Data collected were synthesized qualitatively.Resu...

Research paper thumbnail of Exploring the Impact of Climate Variability on Malaria Transmission Using a Dynamic Mosquito-Human Malaria Model

The Open Infectious Diseases Journal, 2018

Introduction: The reasons for malaria resurgence mostly in Africa are yet to be well understood. ... more Introduction: The reasons for malaria resurgence mostly in Africa are yet to be well understood. Although the causes are often linked to regional climate change, it is important to understand the impact of climate variability on the dynamics of the disease. However, this is almost impossible without adequate long-term malaria data over the study areas. Methods: In this study, we develop a climate-based mosquito-human malaria model to study malaria dynamics in the human population over KwaZulu-Natal, one of the epidemic provinces in South Africa, from 1970-2005. We compare the model output with available observed monthly malaria cases over the province from September 1999 to December 2003. We further use the model outputs to explore the relationship between the climate variables (rainfall and temperature) and malaria incidence over the province using principal component analysis, wavelet power spectrum and wavelet coherence analysis. The model produces a reasonable fit with the obser...

Research paper thumbnail of On the co‐infection of dengue fever and Zika virus

Optimal Control Applications and Methods, 2019

In this paper, we present a co-infection mathematical model for dengue-Zika disease in order to c... more In this paper, we present a co-infection mathematical model for dengue-Zika disease in order to carry out their synergistic relationship in the presence of prevention and treatment. Submodel analysis is investigated to establish the reproduction numbers for each disease and to determine the disease-free local stability equilibrium status. The endemic disease equilibrium is investigated using bifurcation analysis and shows backward bifurcation. We use Pontryagin's maximum principle to explore and determine the best optimal strategies to control both diseases. Numerical optimal control analysis indicates that effective prevention and treatment of each disease will help in the effective control and eradication of the diseases. Finally, the control of co-infection of dengue-Zika requires that communities should combine both prevention and treatment associated with each disease at the same time.

Research paper thumbnail of Exploring the Influence of Daily Climate Variables on Malaria Transmission and Abundance of Anopheles arabiensis over Nkomazi Local Municipality, Mpumalanga Province, South Africa

Journal of Environmental and Public Health, 2018

The recent resurgence of malaria incidence across epidemic regions in South Africa has been linke... more The recent resurgence of malaria incidence across epidemic regions in South Africa has been linked to climatic and environmental factors. An in-depth investigation of the impact of climate variability and mosquito abundance on malaria parasite incidence may therefore offer useful insight towards the control of this life-threatening disease. In this study, we investigate the influence of climatic factors on malaria transmission over Nkomazi Municipality. The variability and interconnectedness between the variables were analyzed using wavelet coherence analysis. Time-series analyses revealed that malaria cases significantly declined after the outbreak in early 2000, but with a slight increase from 2015. Furthermore, the wavelet coherence and time-lagged correlation analyses identified rainfall and abundance of Anopheles arabiensis as the major variables responsible for malaria transmission over the study region. The analysis further highlights a high malaria intensity with the variabl...

Research paper thumbnail of Modeling and analyzing the impact of temperature and rainfall on mosquito population dynamics over Kwazulu-Natal, South Africa

International Journal of Biomathematics, 2017

Malaria parasites are strongly dependent on Anopheles mosquitoes for transmission; for this reaso... more Malaria parasites are strongly dependent on Anopheles mosquitoes for transmission; for this reason, mosquito population dynamics are a crucial determinant of malaria risk. However, temperature and rainfall play a significant role in both aquatic and adult stages of the Anopheles. Consequently, it is important to understand the biology of malaria vector mosquitoes in the study of malaria transmission. In this study, we develop a climate-based, ordinary-differential-equation model to analyze how rainfall and temperature determine mosquito population size. In the model, we consider in detail the influence of ambient temperature on gonotrophic and sporogonic cycles over Amajuba District, Kwazulu-Natal Province, South Africa. In particular, we further use the model to simulate the spatial distribution of the mosquito biting rate over the study region. Our results reflect high seasonality of the population of An. gambiae over the region and also demonstrate the influence of climatic facto...

Research paper thumbnail of Modelling the influence of temperature and rainfall on the population dynamics of Anopheles arabiensis

Malaria Journal, 2016

Background: Malaria continues to be one of the most devastating diseases in the world, killing mo... more Background: Malaria continues to be one of the most devastating diseases in the world, killing more humans than any other infectious disease. Malaria parasites are entirely dependent on Anopheles mosquitoes for transmission. For this reason, vector population dynamics is a crucial determinant of malaria risk. Consequently, it is important to understand the biology of malaria vector mosquitoes in the study of malaria transmission. Temperature and precipitation also play a significant role in both aquatic and adult stages of the Anopheles. Methods: In this study, a climate-based, ordinary-differential-equation model is developed to analyse how temperature and the availability of water affect mosquito population size. In the model, the influence of ambient temperature on the development and the mortality rate of Anopheles arabiensis is considered over a region in KwaZulu-Natal Province, South Africa. In particular, the model is used to examine the impact of climatic factors on the gonotrophic cycle and the dynamics of mosquito population over the study region. Results: The results fairly accurately quantify the seasonality of the population of An. arabiensis over the region and also demonstrate the influence of climatic factors on the vector population dynamics. The model simulates the population dynamics of both immature and adult An. arabiensis. The simulated larval density produces a curve which is similar to observed data obtained from another study. Conclusion: The model is efficiently developed to predict An. arabiensis population dynamics, and to assess the efficiency of various control strategies. In addition, the model framework is built to accommodate human population dynamics with the ability to predict malaria incidence in future.

Research paper thumbnail of Approximate solution of cryptosporidiosis model

Asia Pacific Journal on Computational Engineering, 2016

Background Human cryptosporidiosis is caused by cryptosporidium protozoan and constitutes a large... more Background Human cryptosporidiosis is caused by cryptosporidium protozoan and constitutes a large number of gastrointestinal disease usually connected with recreational water use as the case in Australia [1, 2] as well as other parts of the world [see e.g. [3-6] and references therein]. Cryptosporidiosis is characterized with severe watery diarrhoea; however, asymptomatic infection may arise which becomes the source of infection [1]. Cryptosporidiosis is transmitted through interaction with contaminated water, food and surfaces. Allowing water to get through the mouth into the stomach in recreational swimming is the easiest way of contracting the disease. Crypto is extremely infectious and if not cured one can get the infection again and may infect others. Cryptosporidium is well identified with waterborne transmission mechanism via the faecal-oral path in many recreational water facilities. It is established that the rate of infection is very low in cryptosporidiosis. For instance, it is estimated that it has a low infective dose ranging between 10 and 30 in a healthy adult [7-10]. The disease is capable of resisting to just halogen disinfection which constitutes the recommended level for treating water recreational facilities [11]. If anyone is diagnosed of cryptosporidiosis then the person is likely to have a weak immune system which is a symptom of HIV.

Research paper thumbnail of Co-Dynamics of Trypanosomiasis and Cryptosporidiosis

Applied Mathematics & Information Sciences, 2016

In this paper a mathematical model for trypanosomiasis-cryptosporidium co-infection dynamics is i... more In this paper a mathematical model for trypanosomiasis-cryptosporidium co-infection dynamics is investigated to give a theoretical mathematical account of the impact of cryptosporidiosis on trypanosomiasis dynamics. The model steady states are analyzed. The disease-free equilibrium is shown to be locally asymptotically stable when the associated epidemic basic reproduction number for the model is less than unity. The trypanosomiasis only and the cryptosporidiosis only model are each found to exhibit transcritical and backward bifurcation phenomena respectively. While the co-infection model exhibits the possibility of multiple endemic equilibria. From the sensitivity analysis, the trypanosomiasis reproductive number R lt 0 is more sensitive to δ (death due to insecticides) and crypto parameters whenever R cr 0 > 1 (crypto reproductive number). While the cryptosporidiosis reproductive number R cr 0 is less sensitive to trypanosomiasis parameters whenever R lt 0 > 1 (trypanosomiasis reproductive number). This is an indication that cryptosporidiosis infection may be associated with an increased risk of trypanosomiasis, while trypanosomiasis infection is not associated with an increased risk for cryptosporidiosis. We incorporate time dependent controls, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Furthermore, the effect of the presence of each infection on the endemicity of the other is investigated and presented numerically.

Research paper thumbnail of On the Co-infection of Malaria and Schistosomiasis

Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016

Mathematical models for co-infection of diseases (that is, the simultaneous infection of an indiv... more Mathematical models for co-infection of diseases (that is, the simultaneous infection of an individual by multiple diseases) are sorely lacking in the literature. Here we present a mathematical model for the co-infection of malaria and schistosomiasis. We derive reproduction numbers for malaria and schistosomiasis independently, then combine these to determine the effects of disease interactions. Sensitivity indices show that malaria infection may be associated with an increased rate of schistosomiasis infection. However, schistosomiasis infection is not associated with an increased rate of malaria infection. Therefore, whenever there is co-infection of malaria and schistosomiasis in the community, our model suggests that control measures for each disease should be administered concurrently for effective control.

Research paper thumbnail of Application of mathematical modelling in bioengineering: case study of the design of modified atmosphere packaging for transporting fresh broccoli to consumers

International Journal of Mathematical Modelling and Numerical Optimisation, 2015

In the present study, application of mathematical method to the design of modified atmosphere pac... more In the present study, application of mathematical method to the design of modified atmosphere packaging (MAP) for the transportation of fresh farm produce from a supplier to a retail shop in a distribution chain is presented through a case study involving transportation of fresh broccoli from a supplier to final consumers. The study examined the suitable distribution chain that would ensure the remaining shelf-life of the broccoli meets the consumers' requirement at the time of delivery. The developed model was based on macro-balance of mass and heat transfer. Results from the numerical simulation of the developed model suggest that transportation of the broccoli by air is better than the transportation by water. In addition, a packaging material with oxygen permeability of kO2 = 0.7 kO2max is specified to ensure that the shelf-life of 5 days for the brocolli is met after the delivery.

Research paper thumbnail of Modelling the impact of drug resistance in malaria transmission and its optimal control analysis

International Journal of the Physical Sciences, 2011

We derive and analyse a deterministic model for the transmission of malaria disease with drug res... more We derive and analyse a deterministic model for the transmission of malaria disease with drug resistance in the infectives. Firstly, we calculate the basic reproduction number, R, and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation, with this occurrence, the classical epidemiological requirement for effective eradication of malaria, R < 1, is no longer sufficient, even though necessary. Secondly, by using optimal control theory, we derive the conditions for optimal control of the disease using Pontryagin's Maximum Principle. Finally, numerical simulations are performed to illustrate the analytical results.

Research paper thumbnail of Transmission Dynamics of Hiv/Aids with Optimal Control in the Presence of Carefree Susceptibles and Treatment

Research paper thumbnail of Optimal Seasonal Biocontrol for Eichhornia Crassipes

International Journal of Biomathematics, 2010

This article studies the effect of reduction of an invasive species' competitive ability agai... more This article studies the effect of reduction of an invasive species' competitive ability against another aggressive species, where the intra- and inter-species competition effect on the system is modeled as a control variable. Thus, following the example of competition between water hyacinth–water lettuce, where the competitive ability of the water hyacinth is reduced by the presence of the biological agent Neochetina eichhorniae (weevil) we apply optimal control to compare the effects of the weevil on the competitive relationship. With the effect of the reduced competitive ability been obvious during the larvae stages of the weevil. An objective functional is formulated to minimize the invasive species while minimizing the cost of implementing the control. Numerical results are examined for various parameter values.

Research paper thumbnail of On a drug-resistant malaria model with susceptible individuals without access to basic amenities

Journal of Biological Physics, 2012

In this paper, a deterministic malaria transmission model in the presence of a drug-resistant str... more In this paper, a deterministic malaria transmission model in the presence of a drug-resistant strain is investigated. The model is studied using stability theory of differential equations, optimal control, and computer simulation. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved in the absence of a drug-resistant strain in the population. The existence of multiple endemic equilibria is also established. Both the Sensitivity Index (SI) of the model parameters and the Incremental Cost-Effectiveness Ratio (ICER) for all possible combinations of the disease-control measures are determined. Our results revealed among others that the most cost-effective strategy for drug-resistant malaria control is the combination of the provision of basic amenities (such as access to clean water, electricity, good roads, health care, and education) and treatment of infective individuals. Therefore, more efforts from policy-makers on the provisions of basic amenities and treatment of infectives would go a long way to combat the malaria epidemic.

Research paper thumbnail of Analysis of recruitment and industrial human resources management for optimal productivity in the presence of the HIV/AIDS epidemic

Journal of Biological Physics, 2012

The aim of this paper is to analyze the recruitment effects of susceptible and infected individua... more The aim of this paper is to analyze the recruitment effects of susceptible and infected individuals in order to assess the productivity of an organizational labor force in the presence of HIV/AIDS with preventive and HAART treatment measures in enhancing the workforce output. We consider constant controls as well as time-dependent controls. In the constant control case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit backward and Hopf bifurcations, implying that for the disease to be eradicated, the basic reproductive number must be below a critical value of less than one. We also investigate, by calculating sensitivity indices, the sensitivity of the basic reproductive number to the model's parameters. In the time-dependent control case, we use Pontryagin's maximum principle to derive necessary conditions for the optimal control of the disease. Finally, numerical simulations are performed to illustrate the analytical results. The cost-effectiveness analysis results show that optimal efforts on recruitment (HIV screening of applicants, etc.) is not the most cost-effective strategy to enhance productivity in the organizational labor force. Hence, to enhance employees' productivity, effective education programs and strict adherence to preventive measures should be promoted.

Research paper thumbnail of Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence

Discrete Dynamics in Nature and Society, 2012

The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinea... more The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the sensitivity analysis of the basic reproductive numberR0and the endemic proportions with respect to epidemiological and demographic parameters are provided. From the results of the sensitivity analysis, the model is modified to assess the impact of three control measures; the preventive control to minimize vector human contacts, the treatment control to the infected human, and the insecticide control to the vector. Analytically the existence of the optimal control is established by the use of an optimal control technique and numerically it is solved by an iterative method. Numerical simulations and optimal analysis of the model show that restricted and proper use of control measures might co...

Research paper thumbnail of Mathematical Analysis of a Social Hierarchy-Structured Model for Malaria Transmission Dynamics

SSRN Electronic Journal, 2021

Research paper thumbnail of Application of Optimal Control to the Epidemiology of Fowl Pox Transmission Dynamics in Poultry

Journal of Mathematics and Statistics, 2012

In this study, we present the mathematical model of the transmission dynamics of fowl pox infecti... more In this study, we present the mathematical model of the transmission dynamics of fowl pox infection in poultry. Approach: It describes the interaction between the susceptible and the infected birds which results in a system of ordinary differential equation. Introducing the control which represents the effort in applying chemoprophylaxis control u 1 and treatment control u 2 in birds with fowl pox, the system becomes a system of ordinary differential equations with control. Results: Our optimal control problem involves that in which the number of birds with latent and active fowl pox infections and the cost of treatment controls u 1 (t) and u 2 (t) were minimized subject to the differential Eq. 5-8. This involves the number of birds with active and latent fowl pox respectively as well as the cost of applying chemoprophylaxis control u 1 and treatment u 2 in birds with fowl pox. Conclusion: Analysing the model using Pontryagin's Maximum Principle and optimality conditions, optimal effort necessary to reduce the transmission rate of fowl pox in the poultry has been determined. Hence, it is possible to reduce to reduce the rate of transmission.

Research paper thumbnail of Stability Analysis and Optimal Control of a Lyme Disease Model with Insecticides Spraying and Vaccination

Journal of Biological Systems

This paper studies an SIS-type Lyme transmission model incorporating insecticides spraying and va... more This paper studies an SIS-type Lyme transmission model incorporating insecticides spraying and vaccination as interventions. We obtain the positivity and boundedness of solutions, calculate the basic reproduction number, and discuss the global stability of disease-free and endemic equilibria when the basic reproduction number [Formula: see text] and [Formula: see text], respectively. We apply Pontryagin’s maximum principle to explore an optimal control strategy to minimize the number of infected ticks and hosts and the cost of using insecticides and vaccination. We design numerical simulations to illustrate the effectiveness of theoretical analysis.

Research paper thumbnail of Numerical Investigation of Thermal Stability in a Reactive Sphere of Variable Thermal Conductivity

Thermal stability in a stockpile of combustible material modelled in a spherical domain is invest... more Thermal stability in a stockpile of combustible material modelled in a spherical domain is investigated in this article. The reactive material of the sphere is considered with temperature dependent thermal conductivity and the sphere is assumed to lose heat to the ambient due to exothermic chemical reaction taking place within it. Also, a one-step finite rate irreversible Arrhenius kinetics is assumed to tackle the complicated chemical reaction taking place in this problem. We apply finite difference method (FDM to solve numerically the differential equation governing the problem. FDM is very essential for spatial derivatives discretization. Heat transfer analysis for variation of kinetic parameters embedded within the system, against temperature, is presented graphically and the results are discussed accordingly.

Research paper thumbnail of Investigating the resurgence of malaria prevalence in South Africa between 2015 and 2018: A scoping review

Background Malaria remains a serious concern in most African countries, causing nearly one millio... more Background Malaria remains a serious concern in most African countries, causing nearly one million deaths globally every year. The review aims to examine the extent and nature of the resurgence of malaria prevalence in South Africa.Method Using the Arksey and O'Malley framework, this scoping review included articles published between the year 2015 and 2018 on the resurgence of malaria prevalence in South Africa. Articles were searched from October 2018 to January 2019 using these electronic databases: CINAHL, Pubmed, Science Direct and SCOPUS. Grey literature from Google Scholar was also hand searched. Key search terms and subject headings such as climate variables; climate changes; climatic factors; malaria resurgence; malaria reoccurrence, and malaria increase over epidemic regions in South Africa were used to identify relevant articles. Articles for selection and characterization were performed by three independent reviewers. Data collected were synthesized qualitatively.Resu...

Research paper thumbnail of Exploring the Impact of Climate Variability on Malaria Transmission Using a Dynamic Mosquito-Human Malaria Model

The Open Infectious Diseases Journal, 2018

Introduction: The reasons for malaria resurgence mostly in Africa are yet to be well understood. ... more Introduction: The reasons for malaria resurgence mostly in Africa are yet to be well understood. Although the causes are often linked to regional climate change, it is important to understand the impact of climate variability on the dynamics of the disease. However, this is almost impossible without adequate long-term malaria data over the study areas. Methods: In this study, we develop a climate-based mosquito-human malaria model to study malaria dynamics in the human population over KwaZulu-Natal, one of the epidemic provinces in South Africa, from 1970-2005. We compare the model output with available observed monthly malaria cases over the province from September 1999 to December 2003. We further use the model outputs to explore the relationship between the climate variables (rainfall and temperature) and malaria incidence over the province using principal component analysis, wavelet power spectrum and wavelet coherence analysis. The model produces a reasonable fit with the obser...

Research paper thumbnail of On the co‐infection of dengue fever and Zika virus

Optimal Control Applications and Methods, 2019

In this paper, we present a co-infection mathematical model for dengue-Zika disease in order to c... more In this paper, we present a co-infection mathematical model for dengue-Zika disease in order to carry out their synergistic relationship in the presence of prevention and treatment. Submodel analysis is investigated to establish the reproduction numbers for each disease and to determine the disease-free local stability equilibrium status. The endemic disease equilibrium is investigated using bifurcation analysis and shows backward bifurcation. We use Pontryagin's maximum principle to explore and determine the best optimal strategies to control both diseases. Numerical optimal control analysis indicates that effective prevention and treatment of each disease will help in the effective control and eradication of the diseases. Finally, the control of co-infection of dengue-Zika requires that communities should combine both prevention and treatment associated with each disease at the same time.

Research paper thumbnail of Exploring the Influence of Daily Climate Variables on Malaria Transmission and Abundance of Anopheles arabiensis over Nkomazi Local Municipality, Mpumalanga Province, South Africa

Journal of Environmental and Public Health, 2018

The recent resurgence of malaria incidence across epidemic regions in South Africa has been linke... more The recent resurgence of malaria incidence across epidemic regions in South Africa has been linked to climatic and environmental factors. An in-depth investigation of the impact of climate variability and mosquito abundance on malaria parasite incidence may therefore offer useful insight towards the control of this life-threatening disease. In this study, we investigate the influence of climatic factors on malaria transmission over Nkomazi Municipality. The variability and interconnectedness between the variables were analyzed using wavelet coherence analysis. Time-series analyses revealed that malaria cases significantly declined after the outbreak in early 2000, but with a slight increase from 2015. Furthermore, the wavelet coherence and time-lagged correlation analyses identified rainfall and abundance of Anopheles arabiensis as the major variables responsible for malaria transmission over the study region. The analysis further highlights a high malaria intensity with the variabl...

Research paper thumbnail of Modeling and analyzing the impact of temperature and rainfall on mosquito population dynamics over Kwazulu-Natal, South Africa

International Journal of Biomathematics, 2017

Malaria parasites are strongly dependent on Anopheles mosquitoes for transmission; for this reaso... more Malaria parasites are strongly dependent on Anopheles mosquitoes for transmission; for this reason, mosquito population dynamics are a crucial determinant of malaria risk. However, temperature and rainfall play a significant role in both aquatic and adult stages of the Anopheles. Consequently, it is important to understand the biology of malaria vector mosquitoes in the study of malaria transmission. In this study, we develop a climate-based, ordinary-differential-equation model to analyze how rainfall and temperature determine mosquito population size. In the model, we consider in detail the influence of ambient temperature on gonotrophic and sporogonic cycles over Amajuba District, Kwazulu-Natal Province, South Africa. In particular, we further use the model to simulate the spatial distribution of the mosquito biting rate over the study region. Our results reflect high seasonality of the population of An. gambiae over the region and also demonstrate the influence of climatic facto...

Research paper thumbnail of Modelling the influence of temperature and rainfall on the population dynamics of Anopheles arabiensis

Malaria Journal, 2016

Background: Malaria continues to be one of the most devastating diseases in the world, killing mo... more Background: Malaria continues to be one of the most devastating diseases in the world, killing more humans than any other infectious disease. Malaria parasites are entirely dependent on Anopheles mosquitoes for transmission. For this reason, vector population dynamics is a crucial determinant of malaria risk. Consequently, it is important to understand the biology of malaria vector mosquitoes in the study of malaria transmission. Temperature and precipitation also play a significant role in both aquatic and adult stages of the Anopheles. Methods: In this study, a climate-based, ordinary-differential-equation model is developed to analyse how temperature and the availability of water affect mosquito population size. In the model, the influence of ambient temperature on the development and the mortality rate of Anopheles arabiensis is considered over a region in KwaZulu-Natal Province, South Africa. In particular, the model is used to examine the impact of climatic factors on the gonotrophic cycle and the dynamics of mosquito population over the study region. Results: The results fairly accurately quantify the seasonality of the population of An. arabiensis over the region and also demonstrate the influence of climatic factors on the vector population dynamics. The model simulates the population dynamics of both immature and adult An. arabiensis. The simulated larval density produces a curve which is similar to observed data obtained from another study. Conclusion: The model is efficiently developed to predict An. arabiensis population dynamics, and to assess the efficiency of various control strategies. In addition, the model framework is built to accommodate human population dynamics with the ability to predict malaria incidence in future.

Research paper thumbnail of Approximate solution of cryptosporidiosis model

Asia Pacific Journal on Computational Engineering, 2016

Background Human cryptosporidiosis is caused by cryptosporidium protozoan and constitutes a large... more Background Human cryptosporidiosis is caused by cryptosporidium protozoan and constitutes a large number of gastrointestinal disease usually connected with recreational water use as the case in Australia [1, 2] as well as other parts of the world [see e.g. [3-6] and references therein]. Cryptosporidiosis is characterized with severe watery diarrhoea; however, asymptomatic infection may arise which becomes the source of infection [1]. Cryptosporidiosis is transmitted through interaction with contaminated water, food and surfaces. Allowing water to get through the mouth into the stomach in recreational swimming is the easiest way of contracting the disease. Crypto is extremely infectious and if not cured one can get the infection again and may infect others. Cryptosporidium is well identified with waterborne transmission mechanism via the faecal-oral path in many recreational water facilities. It is established that the rate of infection is very low in cryptosporidiosis. For instance, it is estimated that it has a low infective dose ranging between 10 and 30 in a healthy adult [7-10]. The disease is capable of resisting to just halogen disinfection which constitutes the recommended level for treating water recreational facilities [11]. If anyone is diagnosed of cryptosporidiosis then the person is likely to have a weak immune system which is a symptom of HIV.

Research paper thumbnail of Co-Dynamics of Trypanosomiasis and Cryptosporidiosis

Applied Mathematics & Information Sciences, 2016

In this paper a mathematical model for trypanosomiasis-cryptosporidium co-infection dynamics is i... more In this paper a mathematical model for trypanosomiasis-cryptosporidium co-infection dynamics is investigated to give a theoretical mathematical account of the impact of cryptosporidiosis on trypanosomiasis dynamics. The model steady states are analyzed. The disease-free equilibrium is shown to be locally asymptotically stable when the associated epidemic basic reproduction number for the model is less than unity. The trypanosomiasis only and the cryptosporidiosis only model are each found to exhibit transcritical and backward bifurcation phenomena respectively. While the co-infection model exhibits the possibility of multiple endemic equilibria. From the sensitivity analysis, the trypanosomiasis reproductive number R lt 0 is more sensitive to δ (death due to insecticides) and crypto parameters whenever R cr 0 > 1 (crypto reproductive number). While the cryptosporidiosis reproductive number R cr 0 is less sensitive to trypanosomiasis parameters whenever R lt 0 > 1 (trypanosomiasis reproductive number). This is an indication that cryptosporidiosis infection may be associated with an increased risk of trypanosomiasis, while trypanosomiasis infection is not associated with an increased risk for cryptosporidiosis. We incorporate time dependent controls, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Furthermore, the effect of the presence of each infection on the endemicity of the other is investigated and presented numerically.

Research paper thumbnail of On the Co-infection of Malaria and Schistosomiasis

Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016

Mathematical models for co-infection of diseases (that is, the simultaneous infection of an indiv... more Mathematical models for co-infection of diseases (that is, the simultaneous infection of an individual by multiple diseases) are sorely lacking in the literature. Here we present a mathematical model for the co-infection of malaria and schistosomiasis. We derive reproduction numbers for malaria and schistosomiasis independently, then combine these to determine the effects of disease interactions. Sensitivity indices show that malaria infection may be associated with an increased rate of schistosomiasis infection. However, schistosomiasis infection is not associated with an increased rate of malaria infection. Therefore, whenever there is co-infection of malaria and schistosomiasis in the community, our model suggests that control measures for each disease should be administered concurrently for effective control.

Research paper thumbnail of Application of mathematical modelling in bioengineering: case study of the design of modified atmosphere packaging for transporting fresh broccoli to consumers

International Journal of Mathematical Modelling and Numerical Optimisation, 2015

In the present study, application of mathematical method to the design of modified atmosphere pac... more In the present study, application of mathematical method to the design of modified atmosphere packaging (MAP) for the transportation of fresh farm produce from a supplier to a retail shop in a distribution chain is presented through a case study involving transportation of fresh broccoli from a supplier to final consumers. The study examined the suitable distribution chain that would ensure the remaining shelf-life of the broccoli meets the consumers' requirement at the time of delivery. The developed model was based on macro-balance of mass and heat transfer. Results from the numerical simulation of the developed model suggest that transportation of the broccoli by air is better than the transportation by water. In addition, a packaging material with oxygen permeability of kO2 = 0.7 kO2max is specified to ensure that the shelf-life of 5 days for the brocolli is met after the delivery.

Research paper thumbnail of Modelling the impact of drug resistance in malaria transmission and its optimal control analysis

International Journal of the Physical Sciences, 2011

We derive and analyse a deterministic model for the transmission of malaria disease with drug res... more We derive and analyse a deterministic model for the transmission of malaria disease with drug resistance in the infectives. Firstly, we calculate the basic reproduction number, R, and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation, with this occurrence, the classical epidemiological requirement for effective eradication of malaria, R < 1, is no longer sufficient, even though necessary. Secondly, by using optimal control theory, we derive the conditions for optimal control of the disease using Pontryagin's Maximum Principle. Finally, numerical simulations are performed to illustrate the analytical results.

Research paper thumbnail of Transmission Dynamics of Hiv/Aids with Optimal Control in the Presence of Carefree Susceptibles and Treatment

Research paper thumbnail of Optimal Seasonal Biocontrol for Eichhornia Crassipes

International Journal of Biomathematics, 2010

This article studies the effect of reduction of an invasive species' competitive ability agai... more This article studies the effect of reduction of an invasive species' competitive ability against another aggressive species, where the intra- and inter-species competition effect on the system is modeled as a control variable. Thus, following the example of competition between water hyacinth–water lettuce, where the competitive ability of the water hyacinth is reduced by the presence of the biological agent Neochetina eichhorniae (weevil) we apply optimal control to compare the effects of the weevil on the competitive relationship. With the effect of the reduced competitive ability been obvious during the larvae stages of the weevil. An objective functional is formulated to minimize the invasive species while minimizing the cost of implementing the control. Numerical results are examined for various parameter values.

Research paper thumbnail of On a drug-resistant malaria model with susceptible individuals without access to basic amenities

Journal of Biological Physics, 2012

In this paper, a deterministic malaria transmission model in the presence of a drug-resistant str... more In this paper, a deterministic malaria transmission model in the presence of a drug-resistant strain is investigated. The model is studied using stability theory of differential equations, optimal control, and computer simulation. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved in the absence of a drug-resistant strain in the population. The existence of multiple endemic equilibria is also established. Both the Sensitivity Index (SI) of the model parameters and the Incremental Cost-Effectiveness Ratio (ICER) for all possible combinations of the disease-control measures are determined. Our results revealed among others that the most cost-effective strategy for drug-resistant malaria control is the combination of the provision of basic amenities (such as access to clean water, electricity, good roads, health care, and education) and treatment of infective individuals. Therefore, more efforts from policy-makers on the provisions of basic amenities and treatment of infectives would go a long way to combat the malaria epidemic.

Research paper thumbnail of Analysis of recruitment and industrial human resources management for optimal productivity in the presence of the HIV/AIDS epidemic

Journal of Biological Physics, 2012

The aim of this paper is to analyze the recruitment effects of susceptible and infected individua... more The aim of this paper is to analyze the recruitment effects of susceptible and infected individuals in order to assess the productivity of an organizational labor force in the presence of HIV/AIDS with preventive and HAART treatment measures in enhancing the workforce output. We consider constant controls as well as time-dependent controls. In the constant control case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit backward and Hopf bifurcations, implying that for the disease to be eradicated, the basic reproductive number must be below a critical value of less than one. We also investigate, by calculating sensitivity indices, the sensitivity of the basic reproductive number to the model's parameters. In the time-dependent control case, we use Pontryagin's maximum principle to derive necessary conditions for the optimal control of the disease. Finally, numerical simulations are performed to illustrate the analytical results. The cost-effectiveness analysis results show that optimal efforts on recruitment (HIV screening of applicants, etc.) is not the most cost-effective strategy to enhance productivity in the organizational labor force. Hence, to enhance employees' productivity, effective education programs and strict adherence to preventive measures should be promoted.

Research paper thumbnail of Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence

Discrete Dynamics in Nature and Society, 2012

The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinea... more The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the sensitivity analysis of the basic reproductive numberR0and the endemic proportions with respect to epidemiological and demographic parameters are provided. From the results of the sensitivity analysis, the model is modified to assess the impact of three control measures; the preventive control to minimize vector human contacts, the treatment control to the infected human, and the insecticide control to the vector. Analytically the existence of the optimal control is established by the use of an optimal control technique and numerically it is solved by an iterative method. Numerical simulations and optimal analysis of the model show that restricted and proper use of control measures might co...