Estimating Carrying Capacity in an Aedes aegypti Population Model using Physics-Informed Neural Networks

In South America, the Aedes aegypti mosquito is the main vector of diseases such as dengue, chikungunya, Zika, and yellow fever. To improve mosquito control strategies, we use population models based on ordinary differential equations. An important parameter in these models is the maximum number of eggs in a breeding site, or the carrying capacity K. Attempts have been made to approximate this parameter, but current methods have limitations. In this work, we take advantage of the capability of PINNs to approximate ODEs, to train a PINN that learns a model and in the process approximates the value of K.

We use a population model of female Aedes aegypti mosquitoes based on ODEs, separated into compartments based on two phases of mosquito development, with temperature-dependent parameters. As data for training the PINN, we simulated temperature change over one year to obtain mosquito populations usink K = 1000, then added Gaussian noise. We took 52 weekly samples to simulate field measurements.

The PINN is composed of 5 layers of 128 perceptron elements with Tanh activation. The total loss function is a sum of three components: ODE loss, data loss, and initial condition loss. Across multiple training runs, the best model estimated K as 995.6, achieving a relative error of 0.44%. The learned trajectories closely matched the noisy data.

This work demonstrates that PINNs are useful tools to improve our understanding of mosquito populations and consequently their control, capturing the phenomenology directly from data and governing equations. Future work will incorporate more environmental effects, extend model phases, and analyze parameter approximation under different observability conditions.