Effect of saturated treatment on malaria spread with optimal intervention

Abstract

This work presents a new deterministic model which considers transmission mode through blood transfusion and saturated treatment function with a view to gaining more insights into the dynamical spread of malaria. Existence of steady states of the model is established analytically. The key epidemiological threshold (R0) which determines the potential spread of malaria is computed using the next generation matrix method. The model has a locally asymptotically stable disease-free equilibrium point at R0<1, and condition which ensures the appearance of two endemic equilibria at R0<1 suggesting the possibility of backward bifurcation is determined. It is shown, using Lyapunov function, that a unique endemic equilibrium point is globally asymptotically stable at R0>1. Moreover, the model is modified by incorporating four time-dependent optimal control variables, namely insecticide-treated nets targeted at vector-human transmission route, screening of blood against human–human blood transfusion, anti-malaria drug treatment and vector control with insecticide spraying. Optimal control theory with the aid of Pontryagin’s maximum principle is applied to characterize the optimal control quadruple. Based on efficiency and cost-effectiveness analyses carried out, the most efficient and the most cost-effective combination of the four controls that can be implemented to reduce the burden of malaria in the population are obtained.