A Schistosomiasis Model with Diffusion Effects

Abstract

In this paper, we propose a schistosomiasis model in which two human groups share the water contaminated by schistosomiasis and migrate each other. The dynamical behavior of the model is studied. By calculation, the threshold value is given, which determines whether the disease will be extinct or not. The existence and global stability of the parasite-free equilibrium and the locally stability of the endemic equilibrium are discussed. Numerical simulations indicate that the diffusion from the mild endemic village to severe endemic village is benefit to control schistosomiasis transmission; otherwise it is bad for the disease control.

The Influence of Migration to Regions with Different Coverages of Health Education on Schistosomiasis

“…Certain theoretical guidance for the interruption of block transmission and preventive control of schistosomiasis is provided in China. In view of the current situation of schistosomiasis education in Anhui Province, inspired by the modeling ideas in [20,21], this article distinguishes between the two regions with different coverages of health education on the basis of [26,38,39]. Considering that susceptible and infected populations will migrate between the two regions, the following schistosomiasis model with linear diffusion is constructed:…”

“…[20], the actual phenomenon was considered by Gao et al where two human hosts shared water contaminated by schistosomiasis and migrated with each other, and a schistosomiasis model with migration was established. Studies have shown that the spread of the susceptible population from heavily polluted regions to lightly polluted regions is not conducive to controlling the spread of schistosomiasis [21]. It should be noted that the mutual migration of the susceptible population was considered in two studies [20,21], but the mutual migration of the infected population was not considered.…”

“…Studies have shown that the spread of the susceptible population from heavily polluted regions to lightly polluted regions is not conducive to controlling the spread of schistosomiasis [21]. It should be noted that the mutual migration of the susceptible population was considered in two studies [20,21], but the mutual migration of the infected population was not considered. This mutual migration of patients has an unknown impact on the prevention and control of schistosomiasis, and it is worth exploring.…”