MATHEMATICAL MODELING OF HIV/AIDS DYNAMICS AMONG THE FISHERFOLK AS A VECTOR FOR HIV: A CASE STUDY OF LAKE VICTORIA METAPOPULATIONS

Abstract

HIV/AIDS pandemic has remained the leading causes of death among the sexually transmitted diseases. To date, there has been no cure, and all the intervention measures involve preventive and reduction of the severity of the spread. Several dynamics related to HIV/AIDS have been studied using mathematical models, but the study of the spread of HIV by a vector has not been exhausted. In this study, HIV/AIDS is considered as a human ‘vector borne’ disease, where both the host and the vector is affected. This is possible with the definition of Fisherfolk, as a unique group of people with significantly different disease characteristics, and thus seen to play the role of a vector in the transmission of HIV. This is based on reported high prevalence of HIV among the Fisherfolk, of up to 4 times of the rest of the susceptible. A mathematical model will be formulated, and analyzed to arrive at the following objectives. The first task was to formulate a mathematical model using differential equations to describe human HIV/AIDS disease dynamics of Fisherfolk and normal population around Lake Victoria. The formulated model was then analyzed for the well posedness, in terms of stability, positivity and boundedness to ensure feasible and realistic solutions. In order to optimize the controls, the system was then expressed as a linear programming problem, and used to determine the threshold values of parameters for optimality of disease control measures. Finally, the system was coupled and tested for synchronization, stability and robustness under small perturbation, through All-to-All coupling topology. The achievement of these objectives were realized with the use of the following methods; compartmental formulation of mathematical model, coupling using nearest neighbor and all to all configuration, and use of Lyapunov type numbers to test stability and robustness under small perturbation. The study results found using a system of eight ordinary differential equations that two equilibrium points exists, disease free equilibrium (DFE) and endemic equilibrium point (EEP). DFE was found to be asymptotically stable whenever 𝑅0<1. Intervention strategies like public health education and treatment were found to stabilize periodic solutions of EEP when 𝑅0>1. Synchronization manifold of all to all coupling configuration was determined to be stable under small perturbations with a coupling strength of 𝑘0≥1.1137. This means interaction of a minimum of 12% of the population will lead to synchronization of metapopulations, and therefore any intervention strategy should exceed a threshold of 12% of the population. The findings are valuable to public health and government for planning and budgeting on the desired cost of treating the public, together with other strategies of minimizing interaction through creation of markets, control of fishing points through licensing bottlenecks, and other mitigation strategies to reduce the scourge. This will improve the human resource capacity and improve on fish production in the region.