Mathematical analysis of reinfection and relapse in malaria dynamics

摘要

Recurrent malaria constitutes one of the greatest setbacks to the realization of malaria disease elimination from the population. In this paper, a deterministic model governed by a system of nonlinear differential equations is developed to assess the effects of recurrent malaria – reinfection and relapse on the transmission dynamics of the disease. The model is distributed into autonomous and non-autonomous systems. Analysis of the autonomous model shows that reinfection, which is the recurrence of malaria symptoms due to new parasites infection, has the potential to trigger the existence of two endemic equilibrium points when the basic reproduction number is below unity. Consequently without reinfection, global asymptotic dynamics of the autonomous model is established in the presence of relapse with the aid of carefully constructed Lyapunov functions for both the disease-free and endemic equilibria. The non-autonomous model with time-dependent control strategies is analyzed using Pontryagin’s Maximum Principle to find the optimal solutions to the malaria control problem. Cost-effectiveness analysis is conducted to buttress the results of the optimal control problem by using the average cost-effectiveness ratio (ACER) and incremental cost-effectiveness ratio (ICER) methods. Finally, numerical simulations are demonstrated to enhance the theoretical results.