Dynamics analysis of a malaria transmission model with the influence of temperature and Wolbachia*

Abstract Malaria continues to be a significant global health threat, with periodic outbreaks of varying severity due to Plasmodium infections transmitted by Anopheles mosquitoes. This paper introduces an improved malaria epidemic model, which incorporates the influence of Wolbachia and temperature. And the paper shows that both the disease-free and endemic equilibrium solutions exhibit periodic fluctuations influenced by temperature, aligning with the seasonal patterns observed in malaria transmission, which could explain real-world disease transmission. Additionally, the rigorous dynamical analysis is conducted using Poincaré mapping, periodic semiflow theory and Floquet theory. Specifically, the asymptotic stability of the disease-free periodic solution and the existence of positive periodic solutions are demonstrated in this paper. Finally, numerical simulations corroborate these theoretical results, it is emphasized that the mosquito population will eventually be infected with wolbachia, which has important significance for malaria control.