Mathematical Modelling and Optimal Control of Rabies Transmission Dynamics

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October 10, 2016
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In this thesis, we present an SEIRS model to describe the transmission dynamics of rabies virus in dogs and humans, using optimal control theory. We study the e ect of pre and post-exposure prophylaxis on both compartments. Our analysis shows that the model is mathematically and epidemiologically meaningful, and well-posed. From the analysis, it shows that with an e ective pre-exposure prophylaxis in the human population and the vector population, the rate of rabies transmission will be minimize, and additional control measure on the exposed dogs will minimize the spread of the rabies virus in both compartments, such measures could be post-exposure prophylaxis or culling of exposed dogs. Using the Routh-Hurwitz criterion, it shows that the disease-free equilibrium E0, is locally asymptotically stable, if R0 < 1, applying the Lyapunov function shows that the disease-free equilibrium is globally asymptotically stable, if R0 1, and the endemic equilibrium is global asymptotically stable, if R0 > 1. We also study the controllability of the control model, and then obtain an optimal cost-dependent and time-dependent e ort, to minimize the spread of rabies virus in the exposed and infected classes. The simulation of our 8-di erential equations using the forward-backward sweep scheme and the fourth order Range-Kutta numerical method, shows that applying pre-exposure prophylaxis (vaccination) and post-exposure prophylaxis (treatment) in both compartments have a considerable e ect in reducing the number of infected dogs and humans with rabies than when a single control strategy is use.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the Degree of Master of Philosophy in Applied Mathematics.