Two-patch malaria transmission model: The impact of temperature variability, human mobility and relapse mechanism - Beza Aga; Temesgen Keno; Chernet Deressa (Jambura Journal of Biomathematics (JJBM), 2026)
Malaria remains a major vector-borne infectious disease, particularly in tropical and subtropical regions, where transmission is driven by the bite of Anopheles mosquitoes. Human mobility plays a critical role in shaping the spatial spread of malaria, while temperature variability significantly affects mosquito biting and mortality rates. In this study, we develop and analyze a two-patch compartmental model to investigate the combined impact of temperature variability, human movement, and relapse mechanisms on malaria transmission dynamics across regions with differing endemicity levels. We first verify that the model solutions are non-negative and bounded, confirming the well-posedness of the model from both mathematical and epidemiological perspectives. The next-generation matrix method is used to determine the basic reproduction number, $\mathcal{R}_{0}^{m}$. According to stability analysis, the malaria-free equilibrium is unstable when $\mathcal{R}_{0}^{m} ≥ 1$ and locally and globally asymptotically stable when it is less than unity. This work makes a significant contribution by calibrating the model using reported malaria case data from Ilu Ababor and Gambella, Ethiopia, from 2018 to 2025, which allows for the estimate of critical transmission parameters and model validation. Numerical simulations demonstrate that malaria prevalence is sensitive to both human mobility between patches and temperature variability. The movement of ignorant individuals between patches significantly affects transmission dynamics, as they carry parasites undetected into low-transmission areas and seed new outbreaks. The results further highlight the role of relapse in sustaining transmission. Our findings suggest that targeted control of human movement between high- and low-prevalence regions, combined with environmental monitoring, could significantly reduce the malaria burden.