Analysis of Malaria Control Measures Effectiveness Using Multi-Stage Vector Model

TL;DR

This paper develops a detailed mathematical model to evaluate the effectiveness of various malaria control strategies, analyzing stability and sensitivity to inform cost-effective intervention planning.

Contribution

It introduces a multi-stage vector model incorporating mosquito resting and questing behavior, and analyzes the impact of control measures on disease dynamics.

Findings

If R0<1, the disease-free state is globally stable.

If R0>1, an endemic equilibrium exists and is stable.

Sensitivity analysis identifies key parameters influencing control effectiveness.

Abstract

We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in malaria-endemic areas. The mathematical model consists of a system of several ordinary differential equations, and is based on a multicompartment representation of the system. The model takes into account the mutliple resting-questing stages undergone by adult female mosquitos during the period in which they function as disease vectors. We compute the basic reproduction number $\mathcal R_0$, and show that that if $\mathcal R_0<1$, the disease free equilibrium (DFE) is globally asymptotically stable (GAS) on the non-negative orthant. If $\mathcal R_0>1$, the system admits a unique endemic equilibrium (EE) that is GAS. We perform a sensitivity analysis of the dependence of $\mathcal R_0$ and the EE on parameters related to control measures, such as killing effectiveness and bite prevention. Finally, we discuss the implications for a comprehensive, cost-effective strategy for malaria control.