Global dynamics of a dengue fever model incorporating transmission seasonality

Abstract

The changes of seasons cause that the transmission of dengue fever is characterized by periodicity. We develop a dengue fever transmission model incorporating seasonal periodicity and spatial heterogeneity. Based on the well-posedness of solution for this model, we propose its basic reproduction number R0, and we discuss the properties of this number including its limiting form when the diffusion coefficients change. Moreover, the dynamical behavior of this model infers that if R0 ⩽ 1, then the disease-free periodic solution is globally asymptotically stable, and if R0 > 1, then the model possesses a positive periodic solution, which is globally asymptotically stable. These theoretical findings are further illustrated by the final numerical simulations. Additionally, we add that the similar problem has been investigated by M. Zhu and Y. Xu [A time-periodic dengue fever model in a heterogeneous environment, Math. Comput. Simul., 155:115–129, 2019] in which some dynamical results have been studied only on the cases R0 < 1 and R0 > 1. Our results not only include the scenario on the case R0 = 1, but also involve the more succinct conditions on the cases R0 < 1 and R0 > 1.