Browsing by Author "Mwanga, Gasper G."
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item Mathematical model for optimal control of soil-transmitted helminth infection(Hindawi, 2020) Luboobi, Livingstone; Lambura, Aristide G.; Mwanga, Gasper G.; Kuznetsov, DmitryIn this paper, we study the dynamics of soil-transmitted helminth infection. We formulate and analyse a deterministic compartmental model using nonlinear differential equations. The basic reproduction number is obtained and both disease-free and endemic equilibrium points are shown to be asymptotically stable under given threshold conditions. The model may exhibit backward bifurcation for some parameter values, and the sensitivity indices of the basic reproduction number with respect to the parameters are determined. We extend the model to include control measures for eradication of the infection from the community. Pontryagian’s maximum principle is used to formulate the optimal control problem using three control strategies, namely, health education through provision of educational materials, educational messages to improve the awareness of the susceptible population, and treatment by mass drug administration that target the entire population(preschool- and school-aged children) and sanitation through provision of clean water and personal hygiene. Numerical simulations were done using MATLAB and graphical results are displayed. The cost effectiveness of the control measures were done using incremental cost-effective ratio, and results reveal that the combination of health education and sanitation is the best strategy to combat the helminth infection. Therefore, in order to completely eradicate soil-transmitted helminths, we advise investment efforts on health education and sanitation controls.Item A Mathematical Model for the Dynamics and Cost Effectiveness of the Current Controls of Cassava Brown Streak Disease in Uganda1(J. Math. Comput. Sci, 2015) Kinene, Tonny; Luboobi, Livingstone S.; Nannyonga, Betty; Mwanga, Gasper G.In this paper, Cassava brown streak disease (CBSD), transmitted from white fly vector to the host plant and vice versa, is a major threat to cassava production in Uganda and other cassava growing countries in Africa, e.g. Kenya, Tanzania, Malawi,Mozambique, e.t.c. The seriousness of the situation is that almost all varieties of cassava resistant to cassava mosaic disease (CMD) are susceptible to the new strain of CBSD. Numerous control measures are practiced by farmers, however, the cost effectiveness of these control measures have not been quantified. Therefore it is imperative that we formulate a mathematical model to investigate the transmission dynamics of CBSD and the cost-effectiveness of the control measures. In the analysis of the model we derived the basic reproduction number which helps us in establishing the stability of disease free and endemic equilibrium points. The model is then modified as an optimal control problem with an aim of minimizing the number of infected plants while keeping the cost low. Two time dependent controls are used in the model and an objective function which is a combination of the actual and relative costs associated with the controls is designed. Pontryagins Maximum Principle (PMP) is used to establish the necessary conditions for optimal control of the disease. The incremental cost-effectiveness ratio (ICER) is also computed and used to analyse the cost-effectiveness of the control strategies. Numerical results show that strategy B (uprooting and burning of infected plants) is cost effective, however if the government intervenes with massive spraying, strategy C (spraying with chemicals and uprooting and burning of infected plants) gives the farmer more yield.Item Modeling the Role of Wild Birds And Environment in the Dynamics of Newcastle Disease in Village Chicken(Asian Journal Of Mathematics And Applications, 2018) Chuma, Furaha; Mwanga, Gasper G.; Kajunguri, DamianNewcastle disease is common viral poultry disease which leads to a massive killing of chicken if preventive measures are not well taken. In this paper, we develop and analyze a deterministic model to investigate the role of wild birds and environment on the transmission dynamics of Newcastle disease in village chicken. We compute the basic reproduction number (R0), a threshold that tells the presence of the disease in a population. Finally, we performed the sensitivity analysis of parameters to see their relationship with the basic reproduction number (R0). The numerical results show that the basic reproduction number (R0) is more sensitive to the contact rate between the susceptible village chicken, wild birds and contaminated environment. This implies that, more contamination of the Newcastle virus into the environment increase the chance for the repeatedly occurrence of the disease. The results also shows that increasing the clearance rate of Newcastle disease virus in the environment reduces the rate of spread of the disease in chicken population. Therefore, contaminated environment plays a crucial role in the transmission of Newcastle diseases in the village chicken population.