Analysis of Control Measures for Vector-borne Diseases Using a Multistage Vector Model with Multi-Host Sub-populations

TL;DR

This paper develops a comprehensive multi-stage, multi-host epidemiological model for vector-borne diseases, analyzing disease dynamics and control strategies through differential equations and stability analysis.

Contribution

It introduces a flexible multi-host, multi-stage vector model capable of evaluating various prophylactic measures in vector-borne disease control.

Findings

The basic reproduction number $\\mathcal R_0$ determines disease persistence or eradication.

The disease-free equilibrium is globally stable if $\mathcal R_0 \leq 1$.

An endemic equilibrium exists and is stable if $\mathcal R_0 > 1$.

Abstract

We propose and analyze an epidemiological model for vector borne diseases that integrates a multi-stage vector population and several host sub-populations which may be characterized by a variety of compartmental model types: subpopulations all include Susceptible and Infected compartments, but may or may not include Exposed and/or Recovered compartments. The model was originally designed to evaluate the effectiveness of various prophylactic measures in malaria-endemic areas, but can be applied as well to other vector-borne diseases. This model is expressed as a system of several differential equations, where the number of equations depends on the particular assumptions of the model. We compute the basic reproduction number $\mathcal R_0$, and show that if $\mathcal R_0\leqslant 1$, the disease free equilibrium (DFE) is globally asymptotically stable (GAS) on the nonnegative orthant. If $\mathcal R_0>1$, the system admits a unique endemic equilibrium (EE) that is GAS. We analyze the sensitivity of $R_0$ and the EE to different system parameters, and based on this analysis we discuss the relative effectiveness of different control measures.