Browsing by Author "Mwanga, Gasper Godson"

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Application of Optimal Control Theory to Newcastle Disease Dynamics in Village Chicken by Considering Wild Birds as Reservoir of Disease Virus
(Hindawi, 2019-03-03) Chuma, Furaha; Mwanga, Gasper Godson; Masanja, Verdiana Grace
In this study, an optimal control theory was applied to a nonautonomous model for Newcastle disease transmission in the village chicken population. A notable feature of this model is the inclusion of environment contamination and wild birds, which act as reservoirs of the disease virus. Vaccination, culling, and environmental hygiene and sanitation time dependent control strategies were adopted in the proposed model. This study proved the existence of an optimal control solution, and the necessary conditions for optimality were determined using Pontryagin’s Maximum Principle. The numerical simulations of the optimal control problem were performed using the forward–backward sweep method. The results showed that the use of only the environmental hygiene and sanitation control strategy has no significant effect on the transmission dynamics of the Newcastle disease. Additionally, the combination of vaccination and environmental hygiene and sanitation strategies reduces more number of infected chickens and the concentration of the Newcastle disease virus in the environment than any other combination of control strategies. Furthermore, a cost-effective analysis was performed using the incremental cost-effectiveness ratio method, and the results showed that the use of vaccination alone as the control measure is less costly compared to other control strategies. Hence, the most effective way to minimize the transmission rate of the Newcastle disease and the operational costs is concluded to be the timely vaccination of the entire population of the village chicken, improvement in the sanitation of facilities, and the maintenance of a hygienically clean environment.
Modelling the Transmission Dynamics of Banana Xanthomonas Wilt Disease with Contaminated Soil
(Journal of Mathematics and Informatics, 2019-10-31) Mapinda, John Joel; Mwanga, Gasper Godson; Masanja, Verdiana
Banana Xanthomonas Wilt disease (BXW) is a bacterial disease which highly threaten banana production in east and central Africa. It is caused by a bacteria known as Xanthomonas campestris pv. musacearum (Xcm). Mathematical modelling gives an insight on how to best understand the transmission dynamics and control of the disease. The existing mathematical models have not included contaminated soil in the dynamics of BXW. In this study we formulated a model which includes contaminated soil, calculated the basic reproduction number and carried out sensitivity analysis of some model parameters. We further conducted numerical simulation to validate the results. The simulations show that the infection rate by contaminated farming tools ( i b and e b ), the infection rate by contaminated soil ( 2 w ), vertical disease transmission rate (q ), and the shedding rate of Xcm bacteria in the soil (f ) are positively sensitive to the basic reproduction number. While, the most negative sensitive parameters are the clearance rate of Xcm bacteria from the soil ( h m ), removal of infected plants from the farm ( r ), harvesting ( p a ), and banana plants disease induced death rate ( d ).The result also shows that contaminated soil contributes to the transmission and persistence of BXW disease. Therefore, we recommend that, along with the existing control measures scientist and technologist should carry out studies to find a way to reduce or avoid vertical disease transmission and increase the Xcm clearance rate in the soil. Furthermore, technology for early detection of infected plants should be brought down to the local farmers at affordable costs. This will help stakeholders to detect and remove the infected plants from the farm in time and hence reduce the number of secondary infections.