# Estimating the Size of the Aedes Mosquitoes’ Population Involved in Outbreaks of Dengue and Chikungunya Using a Mathematical Model

## TL;DR

This paper introduces a mathematical model to estimate the population of Aedes mosquitoes during dengue and chikungunya outbreaks using disease incidence data instead of direct mosquito counting.

## Contribution

The model estimates mosquito population size from incidence data, avoiding the logistical challenges of direct counting.

## Key findings

- The model uses a Gaussian Mesa Function to estimate mosquito populations during outbreaks.
- It was successfully applied to dengue and chikungunya data from five cities in Brazil.
- The approach provides a practical alternative to direct mosquito population counting.

## Abstract

Aedes aegypti continues to cause many cases of dengue, chikungunya and Zika fever in affected areas of the tropical world. After being eradicated from Brazil in the decades of 1940 and 1950, Aedes aegypti returned with full force in the early 1970s. Knowing the total number of mosquitoes transmitting Aedes-borne infections is crucial for quantifying the intensity of transmission of these infections. In this paper, we propose a model to estimate the distribution of the number of Aedes mosquitoes’ populations during an outbreak of either dengue or chikungunya. The model assumes that the mosquitoes’ distribution follows a Gaussian Mesa Function (GMF), which has 5 parameters and allows for variable asymmetry. These 5 parameters are adjusted so that they fit indirectly, from a modified Ross‒Macdonald model, the incidence of dengue or chikungunya infections (see main text). Therefore, the observed incidence becomes a function of the parameters of the GMF. We illustrate the model with dengue and chikungunya data from 5 cities in the state of Minas Gerais in the southeastern region of Brazil for the 2023–2024 transmission season. The model shows that it is possible to estimate the size of the mosquitoes’ population from incidence data, circumventing the logistic hurdles involved in the actual counting of mosquitoes. This is the most important practical contribution of this paper. The paper also contains several theoretical innovations, such as a modification of the Ross‒Macdonald model, which is usually presented for a constant mosquitoes’ population, which, of course, is very unrealistic.