AUTHOR=Gizaw Ademe Kebede , Deressa Chernet Tuge TITLE=Fractional-order analysis of temperature- and rainfall-dependent mathematical model for malaria transmission dynamics JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=Volume 10 - 2024 YEAR=2024 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1396650 DOI=10.3389/fams.2024.1396650 ISSN=2297-4687 ABSTRACT=

Malaria remains a substantial public health challenge and economic burden globally. Currently, malaria has been declared as endemic in 85 countries. In this study, we developed and analyzed a fractional-order mathematical model for malaria transmission dynamics that incorporates variability of temperature and rainfall using Caputo-type AB operators. The existence and uniqueness of the model's solutions were established using the Banach fixed-point theorem. The model system's equilibria (both disease-free and endemic) were identified, and lemmas and theorems were developed to prove their stability. Furthermore, we used different temperature ranges and rainfall data, validating them against existing literature. Numerical simulations using the Toufik-Atangana schemes with various fractional-order alpha values revealed that as the value of alpha approaches 1, the behavior of the fractional-order model converges to that of the classical model. The numerical results are promising and are expected to be valuable for future research related to fractional-order models.