Abstract
Based on the real observation data in Tongcheng city, this paper established a mathematical model of schistosomiasis transmission under flood in Anhui province. The delay of schistosomiasis outbreak under flood was considered. Analysis of this model shows that the disease free equilibrium is locally asymptotically stable if the basic reproduction number is less than one. The stability of the unique endemic equilibrium may be changed under some conditions even if the basic reproduction number is larger than one. The impact of flood on the stability of the endemic equilibrium is studied and the results imply that flood can destabilize the system and periodic solutions can arise by Hopf bifurcation. Finally, numerical simulations are performed to support these mathematical results and the results are in accord with the observation data from Tongcheng Schistosomiasis Control Station.
Highlights
As we know, schistosomiasis is a serious water-borne disease
In this paper, based on the observation data in Tongcheng Schistosomiasis Control Station in Anhui province we have modified our previous model by including a time delay that describes the incubation period of schistosome within infected human
We define the basic reproduction number R0 according to biological meanings and give the existence of the disease free equilibrium and the endemic equilibrium
Summary
Schistosomiasis is a serious water-borne disease. It is not easy to control because of many reasons such as flood. Adult schistosomes in human are capable of producing eggs for a number of years [5] This leads to breakout of schistosomiasis in many places after flood. The data from Tongcheng Schistosomiasis Control Station (Figure 1) and the report of Ge et al [1] both show that schistosomiasis is more serious in three years after flood than in the flood year This phenomenon is called the delayed effect of flood [1]. Many schistosomiasis models have involved many aspects such as drug-resistant, age-structure, incubation period of snail, and chemotherapy [6–10]. Their results imply that many factors affect the transmission of schistosomiasis. The goal of this paper is to study the impact of flood on the basic reproduction number and the dynamics of the schistosomiasis transmission.
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