Vector-borne diseases with non-stationary vector populations: the case of growing and decaying populations

TL;DR

This paper develops a vector-borne disease model accounting for non-stationary vector populations, analyzing how growth or decay affects epidemic dynamics and the calculation of the basic reproduction number, R0.

Contribution

It introduces a new epidemic model for growing and decaying vector populations and explores conditions for standard R0 computation and model reduction.

Findings

Growing vector populations delay epidemic peaks.

Standard R0 calculation methods may fail with non-stationary populations.

Model reduction to SIR simplifies parameter estimation.

Abstract

Since the last century, deterministic compartmental models have emerged as powerful tools to predict and control epidemic outbreaks, in many cases helping to mitigate their impacts. A key quantity for these models is the so-called Basic Reproduction Number, that measures the number of secondary infections produced by an initial infected individual in a fully susceptible population. Some methods have been developed to allow the direct computation of this quantity provided that some conditions are fulfilled, such that the model has a pre-pandemic disease-free equilibrium state. This condition is only fulfilled when the populations are stationary. In the case of vector-borne diseases, this implies that the vector birth and death rates need to be balanced, what is not fulfilled in many realistic cases in which the vector population grow or decrease. Here we develop a vector-borne epidemic model with growing and decaying vector populations and study the conditions under which the standard methods to compute $R_0$ work and discuss an alternative when they fail. We also show that growing vector populations produce a delay in the epidemic dynamics when compared to the case of the stationary vector population. Finally, we discuss the conditions under which the model can be reduced to the SIR model with fewer compartments and parameters, which helps in solving the problem of parameter unidentifiability of many vector-borne epidemic models.