Saul Mpeshe - Academia.edu (original) (raw)

Papers by Saul Mpeshe

International Journal of Mathematics and Mathematical Sciences

Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. The disea... more Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. The disease is of public health, veterinary, and economic significance in most of the developed and developing countries. Direct contact between susceptible and infective animals or their contaminated products are the two major routes of the disease transmission. In this paper, we investigate the impacts of controls of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans on the transmission dynamics of Brucellosis. The necessary conditions for an optimal control problem are rigorously analyzed using Pontryagin’s maximum principle. The main ambition is to minimize the spread of brucellosis disease in the community as well as the costs of control strategies. Findings showed that the effective use of livestock vaccination, gradual culling through slaughter of seropositive cattle an...

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New Trends in Mathematical Science

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Computational and Mathematical Methods in Medicine, 2014

A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was consider... more A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was considered to compute the basic reproduction numberℛ0and investigate the impact of temperature and precipitation onℛ0. To study the effect of model parameters toℛ0, sensitivity and elasticity analysis ofℛ0were performed. When temperature and precipitation effects are not considered,ℛ0is more sensitive to the expected number of infectedAedesspp. due to one infected livestock and more elastic to the expected number of infected livestock due to one infectedAedesspp. When climatic data are used,ℛ0is found to be more sensitive and elastic to the expected number of infected eggs laid byAedesspp. via transovarial transmission, followed by the expected number of infected livestock due to one infectedAedesspp. and the expected number of infectedAedesspp. due to one infected livestock for both regions Arusha and Dodoma. These results call for attention to parameters regarding incubation period, the adequa...

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World Journal of Modelling and Simulation, 2018

Typhoid is a major public health concern in many developing countries where safe water supply, fo... more Typhoid is a major public health concern in many developing countries where safe water supply, food hygiene and environmental sanitation are the significant challenges. In this paper, we formulate and analyze a deterministic mathematical model for Typhoid fever with vaccination, screening and treatment of carrier individuals via a system of nonlinear ordinary differential equations. The basic reproductive number is computed and the stability of the disease free equilibrium is investigated. Sensitivity analysis of the reproductive number shows that, the rates of recruitment, screening, treatment of carriers, vaccination, and the rate at which vaccine wanes are the parameters that needs special attention in controlling the disease. The impact of screening and treatment on the basic reproduction number as well as the dynamics of each subpopulation are also investigated through numerical simulations.

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International Journal of Advances in AppliedMathematics andMechanics, 2019

Hepatitis B virus infection remains a major public health concern in many developing countries in... more Hepatitis B virus infection remains a major public health concern in many developing countries in the world. In this paper, we formulate and analyse a simple deterministic model to assess the dynamics and control of the disease using ordinary differential equations. To analyse the effect of the initial transmission of the disease we compute the basic reproduction number R 0 and perform stability analysis. The results show that both the disease-free equilibrium and the endemic equilibrium are globally stable with respect to the value of R 0. Results also show that R 0 is highly affected by the vertical transmission and the recovery rate of the chronic carriers after screening and treatment. Therefore, effective mechanisms which will reduce vertical transmission are needed as well as effective screening of individuals, so that those who will be found infected get treated. Further results from numerical analysis show that when the disease is introduced in the population it is persistent and therefore effective control mechanisms are required. MSC: 00A71 • 93A30 • 93D05 • 93D20 • 97M10

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International Journal of Mathematics and Mathematical Sciences, 2020

Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. e disease... more Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. e disease is of public health, veterinary, and economic significance in most of the developed and developing countries. Direct contact between susceptible and infective animals or their contaminated products are the two major routes of the disease transmission. In this paper, we investigate the impacts of controls of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans on the transmission dynamics of Brucellosis. e necessary conditions for an optimal control problem are rigorously analyzed using Pontryagin's maximum principle. e main ambition is to minimize the spread of brucellosis disease in the community as well as the costs of control strategies. Findings showed that the effective use of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans have a significant impact in minimizing the disease spread in livestock and human populations. Moreover, cost-effectiveness analysis of the controls showed that the combination of livestock vaccination, gradual culling through slaughter, environmental sanitation, and personal protection in humans has high impact and lower cost of prevention.

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Communications in Mathematical Biology and Neuroscience, 2020

Brucellosis is a contagious zoonotic infection caused by bacteria of genus brucella which affects... more Brucellosis is a contagious zoonotic infection caused by bacteria of genus brucella which affects humans and animals. The disease is of veterinary importance, public health concern and economic significance in both developed and developing countries. It is transmitted through direct or indirect contact with infected animals or their contaminated products. In this paper we formulate and analyze a deterministic mathematical model for the transmission dynamics of brucellosis. The model formulated incorporates contaminated environment to human , infected livestock to human, and human to human modes of transmission. The impacts of human treatment in controlling the spread of brucellosis in the human population is investigated. Both analytical and numerical solutions reveal that prolonged human treatment has a significant impact in reducing the spread of Brucellosis in human population only while elimination of the disease in domestic ruminants has promising results to both human and ruminants. Thus, brucellosis control strategies should always focus on elimination of the disease in domestic ruminants.

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New Trends in Mathematical Sciences, 2019

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.

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Computational and Mathematical Methods in Medicine, 2014

A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was consider... more A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was considered to compute the basic reproduction numberℛ0and investigate the impact of temperature and precipitation onℛ0. To study the effect of model parameters toℛ0, sensitivity and elasticity analysis ofℛ0were performed. When temperature and precipitation effects are not considered,ℛ0is more sensitive to the expected number of infectedAedesspp. due to one infected livestock and more elastic to the expected number of infected livestock due to one infectedAedesspp. When climatic data are used,ℛ0is found to be more sensitive and elastic to the expected number of infected eggs laid byAedesspp. via transovarial transmission, followed by the expected number of infected livestock due to one infectedAedesspp. and the expected number of infectedAedesspp. due to one infected livestock for both regions Arusha and Dodoma. These results call for attention to parameters regarding incubation period, the adequa...

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Journal of Mathematical and Computational Science, Aug 26, 2014

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Communications in Optimization Theory, Aug 18, 2014

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Communications in Optimization Theory, Jun 30, 2014

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Acta Biotheoretica

We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatme... more We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin's maximum principle, and it is observed that full treatment effort should be given while increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive...

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Computational and Mathematical Methods in Medicine, 2014

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Acta Biotheoretica, 2011

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International Journal of Mathematics and Mathematical Sciences

Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. The disea... more Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. The disease is of public health, veterinary, and economic significance in most of the developed and developing countries. Direct contact between susceptible and infective animals or their contaminated products are the two major routes of the disease transmission. In this paper, we investigate the impacts of controls of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans on the transmission dynamics of Brucellosis. The necessary conditions for an optimal control problem are rigorously analyzed using Pontryagin’s maximum principle. The main ambition is to minimize the spread of brucellosis disease in the community as well as the costs of control strategies. Findings showed that the effective use of livestock vaccination, gradual culling through slaughter of seropositive cattle an...

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New Trends in Mathematical Science

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Computational and Mathematical Methods in Medicine, 2014

A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was consider... more A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was considered to compute the basic reproduction numberℛ0and investigate the impact of temperature and precipitation onℛ0. To study the effect of model parameters toℛ0, sensitivity and elasticity analysis ofℛ0were performed. When temperature and precipitation effects are not considered,ℛ0is more sensitive to the expected number of infectedAedesspp. due to one infected livestock and more elastic to the expected number of infected livestock due to one infectedAedesspp. When climatic data are used,ℛ0is found to be more sensitive and elastic to the expected number of infected eggs laid byAedesspp. via transovarial transmission, followed by the expected number of infected livestock due to one infectedAedesspp. and the expected number of infectedAedesspp. due to one infected livestock for both regions Arusha and Dodoma. These results call for attention to parameters regarding incubation period, the adequa...

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World Journal of Modelling and Simulation, 2018

Typhoid is a major public health concern in many developing countries where safe water supply, fo... more Typhoid is a major public health concern in many developing countries where safe water supply, food hygiene and environmental sanitation are the significant challenges. In this paper, we formulate and analyze a deterministic mathematical model for Typhoid fever with vaccination, screening and treatment of carrier individuals via a system of nonlinear ordinary differential equations. The basic reproductive number is computed and the stability of the disease free equilibrium is investigated. Sensitivity analysis of the reproductive number shows that, the rates of recruitment, screening, treatment of carriers, vaccination, and the rate at which vaccine wanes are the parameters that needs special attention in controlling the disease. The impact of screening and treatment on the basic reproduction number as well as the dynamics of each subpopulation are also investigated through numerical simulations.

Bookmarks Related papers MentionsView impact

International Journal of Advances in AppliedMathematics andMechanics, 2019

Hepatitis B virus infection remains a major public health concern in many developing countries in... more Hepatitis B virus infection remains a major public health concern in many developing countries in the world. In this paper, we formulate and analyse a simple deterministic model to assess the dynamics and control of the disease using ordinary differential equations. To analyse the effect of the initial transmission of the disease we compute the basic reproduction number R 0 and perform stability analysis. The results show that both the disease-free equilibrium and the endemic equilibrium are globally stable with respect to the value of R 0. Results also show that R 0 is highly affected by the vertical transmission and the recovery rate of the chronic carriers after screening and treatment. Therefore, effective mechanisms which will reduce vertical transmission are needed as well as effective screening of individuals, so that those who will be found infected get treated. Further results from numerical analysis show that when the disease is introduced in the population it is persistent and therefore effective control mechanisms are required. MSC: 00A71 • 93A30 • 93D05 • 93D20 • 97M10

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International Journal of Mathematics and Mathematical Sciences, 2020

Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. e disease... more Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. e disease is of public health, veterinary, and economic significance in most of the developed and developing countries. Direct contact between susceptible and infective animals or their contaminated products are the two major routes of the disease transmission. In this paper, we investigate the impacts of controls of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans on the transmission dynamics of Brucellosis. e necessary conditions for an optimal control problem are rigorously analyzed using Pontryagin's maximum principle. e main ambition is to minimize the spread of brucellosis disease in the community as well as the costs of control strategies. Findings showed that the effective use of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans have a significant impact in minimizing the disease spread in livestock and human populations. Moreover, cost-effectiveness analysis of the controls showed that the combination of livestock vaccination, gradual culling through slaughter, environmental sanitation, and personal protection in humans has high impact and lower cost of prevention.

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Communications in Mathematical Biology and Neuroscience, 2020

Brucellosis is a contagious zoonotic infection caused by bacteria of genus brucella which affects... more Brucellosis is a contagious zoonotic infection caused by bacteria of genus brucella which affects humans and animals. The disease is of veterinary importance, public health concern and economic significance in both developed and developing countries. It is transmitted through direct or indirect contact with infected animals or their contaminated products. In this paper we formulate and analyze a deterministic mathematical model for the transmission dynamics of brucellosis. The model formulated incorporates contaminated environment to human , infected livestock to human, and human to human modes of transmission. The impacts of human treatment in controlling the spread of brucellosis in the human population is investigated. Both analytical and numerical solutions reveal that prolonged human treatment has a significant impact in reducing the spread of Brucellosis in human population only while elimination of the disease in domestic ruminants has promising results to both human and ruminants. Thus, brucellosis control strategies should always focus on elimination of the disease in domestic ruminants.

Bookmarks Related papers MentionsView impact

New Trends in Mathematical Sciences, 2019

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.

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Computational and Mathematical Methods in Medicine, 2014

A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was consider... more A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was considered to compute the basic reproduction numberℛ0and investigate the impact of temperature and precipitation onℛ0. To study the effect of model parameters toℛ0, sensitivity and elasticity analysis ofℛ0were performed. When temperature and precipitation effects are not considered,ℛ0is more sensitive to the expected number of infectedAedesspp. due to one infected livestock and more elastic to the expected number of infected livestock due to one infectedAedesspp. When climatic data are used,ℛ0is found to be more sensitive and elastic to the expected number of infected eggs laid byAedesspp. via transovarial transmission, followed by the expected number of infected livestock due to one infectedAedesspp. and the expected number of infectedAedesspp. due to one infected livestock for both regions Arusha and Dodoma. These results call for attention to parameters regarding incubation period, the adequa...

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Journal of Mathematical and Computational Science, Aug 26, 2014

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Communications in Optimization Theory, Aug 18, 2014

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Communications in Optimization Theory, Jun 30, 2014

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Acta Biotheoretica

We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatme... more We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin's maximum principle, and it is observed that full treatment effort should be given while increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive...

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Computational and Mathematical Methods in Medicine, 2014

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Acta Biotheoretica, 2011

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