Vector-borne disease models with active and inactive vectors: a simple way to consider biting behavior

Abstract

Vector-borne diseases are a serious public health problem, mosquitoes being one of the most important vectors. To analyze the dynamics of this type of disease, Ross–Macdonald models are commonly used. In its simplest formulation and the most common in scientific literature, it is assumed that all mosquitoes are biting at a given rate. To improve this general assumption, we developed a vector-borne disease model with active and inactive vectors as a simple way to incorporate the more general characteristics of mosquito feeding behavior into disease dynamics. Our objective is to obtain an estimate of the Ross–Macdonald biting rate from the feeding parameters that reproduce the same dynamics as the model with active and inactive vectors. Two different cases were analyzed: a SIS–SI model and a SIR–SI model with a single epidemic. Different methods to estimate the biting rate in the Ross–Macdonald model were proposed and analyzed. To compare the results of the models, different epidemiological indicators were considered. When the biting rate is estimated considering that both models have the same basic reproduction number, very similar disease dynamics are obtained. This method is a simple way to incorporate the mosquito feeding behavior into the standard Ross–Macdonald model.