Dynamics of a dengue fever transmission model with crowding effect in human population and spatial variation
Dengue fever is a virus-caused disease in the world. Since the high infection rate of dengue fever and high death rate of its severe form dengue hemorrhagic fever, the control of the spread of the disease is an important issue in the public health. In this paper, authors modify the autonomous system provided in reference [\textit{L. Esteva} and \textit{C. Vargas}, Math. Biosci. 150, No. 2, 131--151 (1998; Zbl 0930.92020)] to obtain a reaction-diffusion system with crowding effect in human population and spatial variation. Authors first study a heterogeneous model with a spatially variable habitat. By the theory of monotone dynamical systems and uniformly persistent, authors obtain threshold number that predicts the disease persistence or extinction. When all the coefficients are habitat independent (i.e. positive constants), the global attractiveness of the steady solutions is discussed by an appropriate Lyapunov function. These findings could be viewed as a generalization to those obtained in reference [loc. cit.]. It is interesting that this paper expounds how the spatial heterogeneity and crowding effect influence the dynamics of the spread of the disease.
scientific article; zbMATH DE number 6146703