Mathematical Model of the Transmission Dynamics of Genital Elephantiasis (Lymphatic Filariasis)

Abstract

This thesis presents a deterministic compartmental model, developed and analyzed to investigate the dynamics of lymphatic filariasis disease, through mosquito-borne infection. The model is in eight compartments: five for the human population and three for the mosquito population based on the microfilariae and antibody levels. The existence of the invariant region where the model is epidemiologically feasible and the positivity of the solution were established. The existence of Disease-free equilibrium (DFE) and the Endemic equilibrium (EE) were determined. Stability analysis of the disease-free equilibrium was investigated via the threshold parameter (reproduction number R_o) obtained using the next generation matrix technique. The model was found to be locally asymptotically stable when the basic reproduction number is less than unity for both special and non special case. It was also revealed that the disease is endemic when R_o > 1. It was proved through Lyapunov method that the DFE and EE are globally asymptotically stable. Simulation analysis was also carried out and it was shown that even when all lymphatic filariasis cases displaying elephantiasis symptoms are put on treatment it will not be able to eradicate the disease. This result suggests that effective control of lymphatic filariasis may lie in treatment for those displaying symptoms. It was also shown that if on the long run as the biting rate of the Mosquitoes increases, the infected population increases. Then as biting rate decreases, then the chronic infected individuals are completely eradicated from the population while the highly infected humans are reduced.  The simulation also showed the impact of the effectiveness of treatment on the chronic infected humans, where we see that the population reduces rigorously until we get to a period of 70 days and then begins to increase again. This shows that the treatment strategies are not effective or perfect. Hence there are chances of fail in treatment. Furthermore our analysis shows that on a long run the trend continues indefinitely.

Key words: Genital Elephantiasis, Mathematical Modeling, Lymphatic filariasis, Endemic Equilibrium (EE)