Dynamics of a dengue model with incubation periods and vertical transmission in a heterogeneous environment

Abstract

Dengue fever is one of the most common insect-borne infectious diseases in the world. In this paper, a dynamics model of dengue fever with incubation periods and vertical transmission in a heterogeneous environment is developed, taking into account the influence of incubation periods and vertical transmission on dengue virus transmission. Theoretically the existence of a global classical solution of the model is proved uniquely, and the threshold dynamics of the model is described using the basic reproduction number R₀. The global asymptotic stability of the disease-free equilibrium is proved by constructing the upper and lower solutions in combination with the properties of the basic reproduction number when R₀ < 1, and the disease-free equilibrium is unstable when R₀ > 1. There exists a global exponential attraction set in the system when R₀ > 1. Finally, numerical simulation and PRCC sensitivity analysis were combined to obtain that increasing the diffusion coefficients of both susceptible and infected populations exacerbates the spread of dengue virus. In reality, dengue virus transmission can be effectively controlled by reducing the frequency of crowd activities, good personal protection against mosquito bites, timely medical treatment, and effective vaccination, among which the reduction of mosquito bite rate has the most significant effect.