Mathematical Model for the Population Dynamics of Aedes aegypti under Extreme Temperature Conditions
Betina Abad *
Faculty of Natural Sciences, National University of Salta, Argentina.
Juan Carlos Rosales
Department of Mathematic, Faculty of Exact Sciences, National University of Salta, Argentina.
*Author to whom correspondence should be addressed.
Abstract
Aims/ Objectives: To develop and analyze a mathematical model for the population dynamics of Aedes aegypti under extreme temperature conditions, focusing on endemic and non-endemic regions of Salta, Argentina.
Study Design: Deterministic mathematical modeling study. Place and Duration of Study: Faculty of Natural Sciences and Faculty of Exact Sciences, National University of Salta, Argentina; simulations and analysis conducted during the research period 2025.
Methodology: Building upon the differential equation framework proposed by Yang et al., entomological parameters were redefined using piecewise continuous functions to extend validity beyond the 10 − 40 ◦C experimental range. This extension is supported by empirical evidence at extreme temperatures, consistent with laboratory observations, thereby ensuring the biological plausibility of the model. The model incorporates larval, pupal, and adult stages. Equilibrium points and stability were analyzed through the Routh–Hurwitz criteria. A local sensitivity analysis of the temperature-dependent basic offspring number \(Q^*_0\) (T) was conducted. This indicator estimates the average number of female mosquitoes produced by a single female at a given temperature after surviving the immature stages, and it differs from the classical basic reproduction number R0, which quantifies the average number of infectious individuals generated in fully susceptible populations. Numerical simulations were performed for three contrasting departments (O´an, Capital, La Poma).
Results: The analysis shows that mosquito persistence or extinction is strongly conditioned by temperature through \(Q^*_0\)(T). Parameters such as oviposition rate, larval survival, and the proportions of larvae and female adults (k and f) are the most influential. Simulations reproduce local patterns: persistence in warmer regions (Or´an, Capital) and extinction in colder regions (La Poma), consistent with field data.
Conclusion: The extended model ensures mathematical consistency under extreme temperatures and provides a consistent framework for predicting vector dynamics in diverse climatic scenarios. These findings strengthen the link between theoretical modeling and empirical evidence, offering relevant implications for public health strategies against dengue in northern Argentina.
Keywords: Aedes, dengue, temperature, modeling, stability, sensitivity