Livingstone Luboobi - Academia.edu (original) (raw)

Papers by Livingstone Luboobi

Mathematical Biosciences, 2018

Enzyme alanine aminotransferase (ALT) elevation which reflects hepatocellular injury is a current... more Enzyme alanine aminotransferase (ALT) elevation which reflects hepatocellular injury is a current challenge in people infected with human immunodeficiency virus (HIV) on antiretroviral therapy (ART). One of the factors that enhance the risk of hepatotoxicity is underlying diseases such as hepatitis caused by hepatitis B virus (HBV). HIV/HBV coinfected patients stand a greater risk of hepatotoxicity because all ART are toxic and liver cells (hepatocytes) that are responsible for metabolising the toxic ART, support all stages of HIV and HBV viral production. Mathematical models coupled with numerical simulations are used in this study with the aim of investigating the optimal combination of ART in HIV/HBV coinfection. Emtricitabine, tenofovir and efavirenz is the optimal combination that maximises the therapeutic effect of therapy and minimises the toxic response to medication in HIV/HBV coinfection.

Asian Journal of Mathematics and Applications, 2014

In this article a continuous time deterministic model with vaccination and treatment strategies i... more In this article a continuous time deterministic model with vaccination and treatment strategies is formulated to assess the effect of reinfection on the transmission dynamics of Tuberculosis (TB). The involvement of reinfection in our model causes relapse and leads to the possibility of backward bifurcation at critical value of effective reproduction number R e =1 and hence the existence of multiple equilibria when effective reproduction number R e <1. This indicates that even by reducing effective reproduction number R e below one is no longer a sufficient condition to eradicate the disease from community. An additional reduction of effective reproduction number R e below the saddle-node bifurcation value is required to eradicate disease from community provided that the disease free equilibrium is globally asymptotically stable. Numerical simulation results are presented to validate analytical results. We suggest that reinfection is an important feature of TB and has to be con...

Asian Journal of Mathematics and Applications, 2017

Maize Lethal Necrosis disease (MLND) is a viral disease that can cause fatal damage to the crop o... more Maize Lethal Necrosis disease (MLND) is a viral disease that can cause fatal damage to the crop of maize plants. This is very common in East Africa countries and Democratic Republic of Congo (DRC). In this manuscript, a mathematical model has been developed to study and analyze the dynamics of the MLND in the maize crop population. The disease free (DFE) and endemic equilibrium (EE) points of the model has been computed and the basic reproduction number ($R_0$) derived using the next generation matrix method. We performed sensitivity analysis by using parametric values from literature and estimated ones. We found that the rates of transmission, lambdamo\lambda_{mo}lambdamo, betao\beta_{{o}}betao and betamm\beta_{mm}betamm are the most positively sensitive parameters. Numerical simulations were also performed to verify the analytical results.Thus, this research work recommends that deliberate strategic intervention should be targeted on the disease transmission rates which are significant for MLND transmission in o...

In this article we apply optimal control theory to one-strain tuberculosis model that incorporate... more In this article we apply optimal control theory to one-strain tuberculosis model that incorporates vaccination and treatment. In this model the control mechanisms associated with chemoprophylaxis of latently infected with TB and education campaign are incorporated in order to reduce the number of latently and actively infected population with TB through application of Pontryagin’s Maximum Principle. Numerical simulations are carried out by using both forward and backward in time fourth order Runge-Kutta schemes. The results show that education campaign control measure alone is more effective in curbing TB transmissions and infections than chemoprophylaxis of latently infected. Furthermore the combination of the two measures has desirable effect of reducing the number of infected individuals with TB than when a single control is used. We suggest that for total eradication of TB from the community, the emphasis of education campaign should be the focal point and chemoprophylaxis of la...

Computational and Mathematical Methods in Medicine, 2019

The emergence of parasite resistance to antimalarial drugs has contributed significantly to globa... more The emergence of parasite resistance to antimalarial drugs has contributed significantly to global human mortality and morbidity due to malaria infection. The impacts of multiple-strain malarial parasite infection have further generated a lot of scientific interest. In this paper, we demonstrate, using the epidemiological model, the effects of parasite resistance and competition between the strains on the dynamics and control of Plasmodium falciparum malaria. The analysed model has a trivial equilibrium point which is locally asymptotically stable when the parasite’s effective reproduction number is less than unity. Using contour plots, we observed that the efficacy of antimalarial drugs used, the rate of development of resistance, and the rate of infection by merozoites are the most important parameters in the multiple-strain P. falciparum infection and control model. Although the drug-resistant strain is shown to be less fit, the presence of both strains in the human host has a hu...

In this paper we analyse the effort dynamics model for Tilapia (Oreochromis niloticus) – Nile per... more In this paper we analyse the effort dynamics model for Tilapia (Oreochromis niloticus) – Nile perch (Lates niloticus) fishery in polluted environment of Tanzanian waters of Lake Victoria. The model is analysed to get the maximum sustainable yield (MSY) points and the corresponding conditions for their existence have been established. The equilibrium points of the model are found with the conditions for their existence being established. The stability analysis of the interior equilibrium point has been investigated by using Routh – Hurwitz criteria method. Later, numerical simulations and their corresponding graphs are presented. It was revealed that the water pollution has significant effects to the maximum sustainable yields of both Tilapia and Nile perch produces. This effect also manifests the rapid changes of efforts invested in harvested the two species at the interior equilibrium point.

In this paper, a mathematical model on the interaction between hepatitis c virus (HCV) and immune... more In this paper, a mathematical model on the interaction between hepatitis c virus (HCV) and immune system has been studied. The paper intends to upgrade the model developed by Avendano et al.(2002) by including death of hepatocytes due to infection and spontaneous clearance of viruses by a noncytolytic process during acute stage of the HCV infection. The next generation matrix method has been applied to compute the basic reproductive number. Also, the stability analysis of the system has been performed for the existence of the disease free and endemic equilibrium states using Meltzer matrix, Routh-Hurwitz and Lyapunov methods. The results indicate that the disease free equilibrium state is locally asymptotically stable if, and unstable if.The endemic equilibrium state is both locally and globally asymptotically stable. We calculated the sensitivity indices of the dynamic threshold relating to each parameter in the model, where we found that the decrease of the rate of infection and t...

Results in Applied Mathematics, 2021

New Trends in Mathematical Science, 2017

Computational and Mathematical Methods in Medicine

Globally, it is estimated that of the 36.7 million people infected with human immunodeficiency vi... more Globally, it is estimated that of the 36.7 million people infected with human immunodeficiency virus (HIV), 6.3% are coinfected with hepatitis C virus (HCV). Coinfection with HIV reduces the chance of HCV spontaneous clearance. In this work, we formulated and analysed a deterministic model to study the HIV and HCV coinfection dynamics in absence of therapy. Due to chronic stage of HCV infection being long, asymptomatic, and infectious, our model formulation was based on the splitting of the chronic stage into the following: before onset of cirrhosis and its complications and after onset of cirrhosis. We computed the basic reproduction numbers using the next generation matrix method. We performed numerical simulations to support the analytical results. We carried out sensitivity analysis to determine the relative importance of the different parameters influencing the HIV-HCV coinfection dynamics. The findings reveal that, in the long run, there is a substantial number of individuals ...

Asian Journal of Mathematics and Applications, 2017

Tungiasis refers to the infestation caused by the permanent penetration of the female sand flea “... more Tungiasis refers to the infestation caused by the permanent penetration of the female sand flea “ Tunga penetrans ” into the skin of the human or animal hosts and causes cutaneous lesion. In this paper, we developed a deterministic model for the dynamics of tungiasis in communities of human beings, animal reservoirs and flea infested environment in order to understand the way tungiasis disease spreads in a poor resource community. We established the conditions for local and global stability of the disease-free and endemic equilibrium points. The computational results showed that the disease-free equilibrium point is locally and globally asymptotically stable when the model basic reproduction number is less than unit, that is. Using the Lyapunov stability theory and LaSalle’s Invariant Principle we found that the endemic equilibrium point (EE) is globally asymptotically stable when. The numerical simulations have been presented to illustrate the way the model variables behave when t...

In this paper, a simple model for the effect of tobacco smoking in the in-host dynamics of HIV is... more In this paper, a simple model for the effect of tobacco smoking in the in-host dynamics of HIV is formulated with the aim of studying how tobacco smoking affects HIV in-host dynamics. The basic reproduction number here known as smoking induced reproduction number R0is computed, disease free and endemic equilibria are derived and conditions for their stability are established. Analytical results show that smoking affects both T-cells and Macrophages however, its effects are severe in macrophages than in T-cells. Stability for disease free and endemic equilibria is analyzed. High smoking rate renders disease free equilibrium to be locally and globally unstable. Low smoking rate leads to globally unstable endemic equilibrium. Numerical results reveal that tobacco smoking which confers insensitivity to T-cells and reducing phagocytosis in macrophages can promote in-host HIV dynamics.

Journal of Mathematics and Informatics

Brucellosis is a zoonotic bacterial infection that can be acquired by humans from infected animal... more Brucellosis is a zoonotic bacterial infection that can be acquired by humans from infected animals' meat, urine, body fluids, aborted materials, unpasteurized milk, and milk products or contaminated environment. Mathematical models for infectious diseases have been used as important tools in providing useful information regarding the transmission and effectiveness of the available control strategies. In this paper, a review of the available compartmental mathematical models for Brucellosis was done. The main purpose was to assess their structure, populations involved, the available control strategies and suitability in predicting the disease incidence and prevalence in different settings. Diversities have been observed in the reviewed mathematical models; some models incorporated seasonal variations in a single animal population, some ignored the contributions of the contaminated environment while others considered the cattle or sheep population only. Most of the models reviewed have not considered the contribution of wild animals in the dynamics of Brucellosis. Some models do not match the real situation in most affected areas like sub-Saharan African region and Asian countries where wild animals, cattle and small ruminants share grazing areas and water points. Thus, to avoid unreliable results, this review reveals the need to affirm and incorporate wild animals, livestock, humans and seasonal weather parameters in the spread of Brucellosis and in planning for its controls.

New Trends in Mathematical Science

Brucellosis is a neglected zoonotic infection caused by gram-negative bacteria of genus brucella.... more Brucellosis is a neglected zoonotic infection caused by gram-negative bacteria of genus brucella. In this paper, a deterministic mathematical model for the infectiology of brucellosis with vaccination of ruminants, culling of seropositive animals through slaughter, and proper environmental hygiene and sanitation is formulated and analyzed. A positive invariant region of the formulated model is established using the Box Invariance method, the effective reproduction number, R e of the model is computed using the standard next generation approach. We prove that the brucellosis free equilibrium exists, locally and globally asymptotically stable if R e < 1 while the endemic equilibrium point exists, locally and globally asymptotically stable if R e > 1. Sensitivity analysis of the effective reproductive number shows that, natural mortality rate of ruminants, recruitment rate, ruminant to ruminant transmission rate, vaccination rate, and disease induced culling rate are the most sensitive parameters and should be targeted in designing of the control strategies for the disease. Numerical simulation is done to show the variations of each subpopulation with respect to the control parameters.

International scholarly research notices, 2017

Thedynamics of HIV infection, the infection mechanism, the cell types infected, and the role play... more Thedynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having< 1. Lastly, the biological dynamics of HIVinfection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral r...

Computational and Mathematical Methods in Medicine, 2006

An HIV/AIDS model incorporating complacency for the adult population is formulated. Complacency i... more An HIV/AIDS model incorporating complacency for the adult population is formulated. Complacency is assumed a function of number of AIDS cases in a community with an inverse relation. A method to find the equilibrium state of the model is given by proving a stated theorem. An example to illustrate use of the theorem is also given. Model analysis and simulations show that complacency resulting from dependence of HIV transmission on number of AIDS cases in a community leads to damped periodic oscillations in the number of infectives with oscillations more marked at lower rates of progression to AIDS. The implications of these results to public health with respect to monitoring the HIV/AIDS epidemic and widespread use of antiretroviral (ARV) drugs is discussed.

A deterministic model for the dynamics of malaria and HIV co-infection with protective measures i... more A deterministic model for the dynamics of malaria and HIV co-infection with protective measures is developed. We extend the model to incorporate HIV positive immigrants into the community. The model is analysed and threshold values deter- mined. Results from the model show that there is no disease-free point. Instead, an initial infection state governed by the infective immigration rateexists. A small perturbation around this point approaches global stability if there is reduced susceptibility to HIV by malaria infected individuals. Similarly, if HIV infectives are protected against malaria, the system attains global stability. It is shown that both diseases co-exist if the prevalence of one disease is low and the other high. From the results it is concluded that individuals protect themselves against malaria more when prevalence is high. The major finding of this study is that contrary to the malaria case, HIV positive individuals tend not to use protection when there is increased ...

Journal of Mathematical and Computational Science, 2017

Malaria is one of infectious diseases that kill a large number of people worldwide, mostly in sub... more Malaria is one of infectious diseases that kill a large number of people worldwide, mostly in sub-Saharan Africa. Recently, mathematical models on the in-human host dynamics of malaria has increasingly attracted researchers’ interests. This study proposed a mathematical model to describe in-human host and in-mosquito dynamics of malaria. The expression of the basic reproduction number, R0 of this model is established. Sensitivity analysis of R0 with respect to each of the parameters is carried out in model validation. Effects of parameters of R0 was discussed to determine their implications in the control of malaria infection. Infection rate of red blood cells (RBCs) by merozoites, the death rate of merozoites, number of merozoites released per rupturing schizont were found to be crucial parameters in control strategies. Moreover, a number of merozoites released per rupturing schizont and the proportion of merozoites that proceed with asexual replication are the most sensitive param...

Journal of Mathematics and Computer Science, 2017

The object of the present paper is to study of radius of convexity two certain integral operators... more The object of the present paper is to study of radius of convexity two certain integral operators as follows F (z) := z 0 n i=1 f ′ i (t) γ i dt and J(z) := z 0 n i=1 f ′ i (t) γ i m j=1 g j (z) z λ j dt, where γ i , λ i ∈ C, f i (1 ≤ i ≤ n) and g j (1 ≤ j ≤ m) belong to the certain subclass of analytic functions. 2010 Mathematics Subject Classification. 30C45.

In this article we apply optimal control theory to one-strain tuberculosis model that incorporate... more In this article we apply optimal control theory to one-strain tuberculosis model that incorporates vaccination and treatment. In this model the control mechanisms associated with chemoprophylaxis of latently infected with TB and education campaign are incorporated in order to reduce the number of latently and actively infected population with TB through application of Pontryagin's Maximum Principle. Numerical simulations are carried out by using both forward and backward in time fourth order Runge-Kutta schemes. The results show that education campaign control measure alone is more effective in curbing TB transmissions and infections than chemoprophylaxis of latently infected. Furthermore the combination of the two measures has desirable effect of reducing the number of infected individuals with TB than when a single control is used. We suggest that for total eradication of TB from the community, the emphasis of education campaign should be the focal point and chemoprophylaxis o...

Mathematical Biosciences, 2018

Enzyme alanine aminotransferase (ALT) elevation which reflects hepatocellular injury is a current... more Enzyme alanine aminotransferase (ALT) elevation which reflects hepatocellular injury is a current challenge in people infected with human immunodeficiency virus (HIV) on antiretroviral therapy (ART). One of the factors that enhance the risk of hepatotoxicity is underlying diseases such as hepatitis caused by hepatitis B virus (HBV). HIV/HBV coinfected patients stand a greater risk of hepatotoxicity because all ART are toxic and liver cells (hepatocytes) that are responsible for metabolising the toxic ART, support all stages of HIV and HBV viral production. Mathematical models coupled with numerical simulations are used in this study with the aim of investigating the optimal combination of ART in HIV/HBV coinfection. Emtricitabine, tenofovir and efavirenz is the optimal combination that maximises the therapeutic effect of therapy and minimises the toxic response to medication in HIV/HBV coinfection.

Asian Journal of Mathematics and Applications, 2014

In this article a continuous time deterministic model with vaccination and treatment strategies i... more In this article a continuous time deterministic model with vaccination and treatment strategies is formulated to assess the effect of reinfection on the transmission dynamics of Tuberculosis (TB). The involvement of reinfection in our model causes relapse and leads to the possibility of backward bifurcation at critical value of effective reproduction number R e =1 and hence the existence of multiple equilibria when effective reproduction number R e <1. This indicates that even by reducing effective reproduction number R e below one is no longer a sufficient condition to eradicate the disease from community. An additional reduction of effective reproduction number R e below the saddle-node bifurcation value is required to eradicate disease from community provided that the disease free equilibrium is globally asymptotically stable. Numerical simulation results are presented to validate analytical results. We suggest that reinfection is an important feature of TB and has to be con...

Asian Journal of Mathematics and Applications, 2017

Maize Lethal Necrosis disease (MLND) is a viral disease that can cause fatal damage to the crop o... more Maize Lethal Necrosis disease (MLND) is a viral disease that can cause fatal damage to the crop of maize plants. This is very common in East Africa countries and Democratic Republic of Congo (DRC). In this manuscript, a mathematical model has been developed to study and analyze the dynamics of the MLND in the maize crop population. The disease free (DFE) and endemic equilibrium (EE) points of the model has been computed and the basic reproduction number ($R_0$) derived using the next generation matrix method. We performed sensitivity analysis by using parametric values from literature and estimated ones. We found that the rates of transmission, lambdamo\lambda_{mo}lambdamo, betao\beta_{{o}}betao and betamm\beta_{mm}betamm are the most positively sensitive parameters. Numerical simulations were also performed to verify the analytical results.Thus, this research work recommends that deliberate strategic intervention should be targeted on the disease transmission rates which are significant for MLND transmission in o...

In this article we apply optimal control theory to one-strain tuberculosis model that incorporate... more In this article we apply optimal control theory to one-strain tuberculosis model that incorporates vaccination and treatment. In this model the control mechanisms associated with chemoprophylaxis of latently infected with TB and education campaign are incorporated in order to reduce the number of latently and actively infected population with TB through application of Pontryagin’s Maximum Principle. Numerical simulations are carried out by using both forward and backward in time fourth order Runge-Kutta schemes. The results show that education campaign control measure alone is more effective in curbing TB transmissions and infections than chemoprophylaxis of latently infected. Furthermore the combination of the two measures has desirable effect of reducing the number of infected individuals with TB than when a single control is used. We suggest that for total eradication of TB from the community, the emphasis of education campaign should be the focal point and chemoprophylaxis of la...

Computational and Mathematical Methods in Medicine, 2019

The emergence of parasite resistance to antimalarial drugs has contributed significantly to globa... more The emergence of parasite resistance to antimalarial drugs has contributed significantly to global human mortality and morbidity due to malaria infection. The impacts of multiple-strain malarial parasite infection have further generated a lot of scientific interest. In this paper, we demonstrate, using the epidemiological model, the effects of parasite resistance and competition between the strains on the dynamics and control of Plasmodium falciparum malaria. The analysed model has a trivial equilibrium point which is locally asymptotically stable when the parasite’s effective reproduction number is less than unity. Using contour plots, we observed that the efficacy of antimalarial drugs used, the rate of development of resistance, and the rate of infection by merozoites are the most important parameters in the multiple-strain P. falciparum infection and control model. Although the drug-resistant strain is shown to be less fit, the presence of both strains in the human host has a hu...

In this paper we analyse the effort dynamics model for Tilapia (Oreochromis niloticus) – Nile per... more In this paper we analyse the effort dynamics model for Tilapia (Oreochromis niloticus) – Nile perch (Lates niloticus) fishery in polluted environment of Tanzanian waters of Lake Victoria. The model is analysed to get the maximum sustainable yield (MSY) points and the corresponding conditions for their existence have been established. The equilibrium points of the model are found with the conditions for their existence being established. The stability analysis of the interior equilibrium point has been investigated by using Routh – Hurwitz criteria method. Later, numerical simulations and their corresponding graphs are presented. It was revealed that the water pollution has significant effects to the maximum sustainable yields of both Tilapia and Nile perch produces. This effect also manifests the rapid changes of efforts invested in harvested the two species at the interior equilibrium point.

In this paper, a mathematical model on the interaction between hepatitis c virus (HCV) and immune... more In this paper, a mathematical model on the interaction between hepatitis c virus (HCV) and immune system has been studied. The paper intends to upgrade the model developed by Avendano et al.(2002) by including death of hepatocytes due to infection and spontaneous clearance of viruses by a noncytolytic process during acute stage of the HCV infection. The next generation matrix method has been applied to compute the basic reproductive number. Also, the stability analysis of the system has been performed for the existence of the disease free and endemic equilibrium states using Meltzer matrix, Routh-Hurwitz and Lyapunov methods. The results indicate that the disease free equilibrium state is locally asymptotically stable if, and unstable if.The endemic equilibrium state is both locally and globally asymptotically stable. We calculated the sensitivity indices of the dynamic threshold relating to each parameter in the model, where we found that the decrease of the rate of infection and t...

Results in Applied Mathematics, 2021

New Trends in Mathematical Science, 2017

Computational and Mathematical Methods in Medicine

Globally, it is estimated that of the 36.7 million people infected with human immunodeficiency vi... more Globally, it is estimated that of the 36.7 million people infected with human immunodeficiency virus (HIV), 6.3% are coinfected with hepatitis C virus (HCV). Coinfection with HIV reduces the chance of HCV spontaneous clearance. In this work, we formulated and analysed a deterministic model to study the HIV and HCV coinfection dynamics in absence of therapy. Due to chronic stage of HCV infection being long, asymptomatic, and infectious, our model formulation was based on the splitting of the chronic stage into the following: before onset of cirrhosis and its complications and after onset of cirrhosis. We computed the basic reproduction numbers using the next generation matrix method. We performed numerical simulations to support the analytical results. We carried out sensitivity analysis to determine the relative importance of the different parameters influencing the HIV-HCV coinfection dynamics. The findings reveal that, in the long run, there is a substantial number of individuals ...

Asian Journal of Mathematics and Applications, 2017

Tungiasis refers to the infestation caused by the permanent penetration of the female sand flea “... more Tungiasis refers to the infestation caused by the permanent penetration of the female sand flea “ Tunga penetrans ” into the skin of the human or animal hosts and causes cutaneous lesion. In this paper, we developed a deterministic model for the dynamics of tungiasis in communities of human beings, animal reservoirs and flea infested environment in order to understand the way tungiasis disease spreads in a poor resource community. We established the conditions for local and global stability of the disease-free and endemic equilibrium points. The computational results showed that the disease-free equilibrium point is locally and globally asymptotically stable when the model basic reproduction number is less than unit, that is. Using the Lyapunov stability theory and LaSalle’s Invariant Principle we found that the endemic equilibrium point (EE) is globally asymptotically stable when. The numerical simulations have been presented to illustrate the way the model variables behave when t...

In this paper, a simple model for the effect of tobacco smoking in the in-host dynamics of HIV is... more In this paper, a simple model for the effect of tobacco smoking in the in-host dynamics of HIV is formulated with the aim of studying how tobacco smoking affects HIV in-host dynamics. The basic reproduction number here known as smoking induced reproduction number R0is computed, disease free and endemic equilibria are derived and conditions for their stability are established. Analytical results show that smoking affects both T-cells and Macrophages however, its effects are severe in macrophages than in T-cells. Stability for disease free and endemic equilibria is analyzed. High smoking rate renders disease free equilibrium to be locally and globally unstable. Low smoking rate leads to globally unstable endemic equilibrium. Numerical results reveal that tobacco smoking which confers insensitivity to T-cells and reducing phagocytosis in macrophages can promote in-host HIV dynamics.

Journal of Mathematics and Informatics

Brucellosis is a zoonotic bacterial infection that can be acquired by humans from infected animal... more Brucellosis is a zoonotic bacterial infection that can be acquired by humans from infected animals' meat, urine, body fluids, aborted materials, unpasteurized milk, and milk products or contaminated environment. Mathematical models for infectious diseases have been used as important tools in providing useful information regarding the transmission and effectiveness of the available control strategies. In this paper, a review of the available compartmental mathematical models for Brucellosis was done. The main purpose was to assess their structure, populations involved, the available control strategies and suitability in predicting the disease incidence and prevalence in different settings. Diversities have been observed in the reviewed mathematical models; some models incorporated seasonal variations in a single animal population, some ignored the contributions of the contaminated environment while others considered the cattle or sheep population only. Most of the models reviewed have not considered the contribution of wild animals in the dynamics of Brucellosis. Some models do not match the real situation in most affected areas like sub-Saharan African region and Asian countries where wild animals, cattle and small ruminants share grazing areas and water points. Thus, to avoid unreliable results, this review reveals the need to affirm and incorporate wild animals, livestock, humans and seasonal weather parameters in the spread of Brucellosis and in planning for its controls.

New Trends in Mathematical Science

Brucellosis is a neglected zoonotic infection caused by gram-negative bacteria of genus brucella.... more Brucellosis is a neglected zoonotic infection caused by gram-negative bacteria of genus brucella. In this paper, a deterministic mathematical model for the infectiology of brucellosis with vaccination of ruminants, culling of seropositive animals through slaughter, and proper environmental hygiene and sanitation is formulated and analyzed. A positive invariant region of the formulated model is established using the Box Invariance method, the effective reproduction number, R e of the model is computed using the standard next generation approach. We prove that the brucellosis free equilibrium exists, locally and globally asymptotically stable if R e < 1 while the endemic equilibrium point exists, locally and globally asymptotically stable if R e > 1. Sensitivity analysis of the effective reproductive number shows that, natural mortality rate of ruminants, recruitment rate, ruminant to ruminant transmission rate, vaccination rate, and disease induced culling rate are the most sensitive parameters and should be targeted in designing of the control strategies for the disease. Numerical simulation is done to show the variations of each subpopulation with respect to the control parameters.

International scholarly research notices, 2017

Thedynamics of HIV infection, the infection mechanism, the cell types infected, and the role play... more Thedynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having< 1. Lastly, the biological dynamics of HIVinfection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral r...

Computational and Mathematical Methods in Medicine, 2006

An HIV/AIDS model incorporating complacency for the adult population is formulated. Complacency i... more An HIV/AIDS model incorporating complacency for the adult population is formulated. Complacency is assumed a function of number of AIDS cases in a community with an inverse relation. A method to find the equilibrium state of the model is given by proving a stated theorem. An example to illustrate use of the theorem is also given. Model analysis and simulations show that complacency resulting from dependence of HIV transmission on number of AIDS cases in a community leads to damped periodic oscillations in the number of infectives with oscillations more marked at lower rates of progression to AIDS. The implications of these results to public health with respect to monitoring the HIV/AIDS epidemic and widespread use of antiretroviral (ARV) drugs is discussed.

A deterministic model for the dynamics of malaria and HIV co-infection with protective measures i... more A deterministic model for the dynamics of malaria and HIV co-infection with protective measures is developed. We extend the model to incorporate HIV positive immigrants into the community. The model is analysed and threshold values deter- mined. Results from the model show that there is no disease-free point. Instead, an initial infection state governed by the infective immigration rateexists. A small perturbation around this point approaches global stability if there is reduced susceptibility to HIV by malaria infected individuals. Similarly, if HIV infectives are protected against malaria, the system attains global stability. It is shown that both diseases co-exist if the prevalence of one disease is low and the other high. From the results it is concluded that individuals protect themselves against malaria more when prevalence is high. The major finding of this study is that contrary to the malaria case, HIV positive individuals tend not to use protection when there is increased ...

Journal of Mathematical and Computational Science, 2017

Malaria is one of infectious diseases that kill a large number of people worldwide, mostly in sub... more Malaria is one of infectious diseases that kill a large number of people worldwide, mostly in sub-Saharan Africa. Recently, mathematical models on the in-human host dynamics of malaria has increasingly attracted researchers’ interests. This study proposed a mathematical model to describe in-human host and in-mosquito dynamics of malaria. The expression of the basic reproduction number, R0 of this model is established. Sensitivity analysis of R0 with respect to each of the parameters is carried out in model validation. Effects of parameters of R0 was discussed to determine their implications in the control of malaria infection. Infection rate of red blood cells (RBCs) by merozoites, the death rate of merozoites, number of merozoites released per rupturing schizont were found to be crucial parameters in control strategies. Moreover, a number of merozoites released per rupturing schizont and the proportion of merozoites that proceed with asexual replication are the most sensitive param...

Journal of Mathematics and Computer Science, 2017

The object of the present paper is to study of radius of convexity two certain integral operators... more The object of the present paper is to study of radius of convexity two certain integral operators as follows F (z) := z 0 n i=1 f ′ i (t) γ i dt and J(z) := z 0 n i=1 f ′ i (t) γ i m j=1 g j (z) z λ j dt, where γ i , λ i ∈ C, f i (1 ≤ i ≤ n) and g j (1 ≤ j ≤ m) belong to the certain subclass of analytic functions. 2010 Mathematics Subject Classification. 30C45.

In this article we apply optimal control theory to one-strain tuberculosis model that incorporate... more In this article we apply optimal control theory to one-strain tuberculosis model that incorporates vaccination and treatment. In this model the control mechanisms associated with chemoprophylaxis of latently infected with TB and education campaign are incorporated in order to reduce the number of latently and actively infected population with TB through application of Pontryagin's Maximum Principle. Numerical simulations are carried out by using both forward and backward in time fourth order Runge-Kutta schemes. The results show that education campaign control measure alone is more effective in curbing TB transmissions and infections than chemoprophylaxis of latently infected. Furthermore the combination of the two measures has desirable effect of reducing the number of infected individuals with TB than when a single control is used. We suggest that for total eradication of TB from the community, the emphasis of education campaign should be the focal point and chemoprophylaxis o...