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A mathematical model for the seasonal transmission of schistosomiasis in the lake and marshland regions of China

a. College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China
b. College of Mathematics and Physics, Xinjiang Agriculture University, Urumqi, Xinjiang 830052, China
c. Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA
d. Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, China
e. Department of Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China

Schistosomiasis, a parasitic disease caused by Schistosoma Japonicum, is still one of the most serious parasitic diseases in China and remains endemic in seven provinces, including Hubei, Anhui, Hunan, Jiangsu, Jiangxi, Sichuan, and Yunnan. The monthly data of human schistosomiasis cases in Hubei, Hunan, and Anhui provinces (lake and marshland regions) released by the Chinese Center for Disease Control and Prevention (China CDC) display a periodic pattern with more cases in late summer and early autumn. Based on this observation, we construct a deterministic model with periodic transmission rates to study the seasonal transmission dynamics of schistosomiasis in these lake and marshland regions in China. We calculate the basic reproduction number $R_{0}$, discuss the dynamical behavior of solutions to the model, and use the model to fit the monthly data of human schistosomiasis cases in Hubei. We also perform some sensitivity analysis of the basic reproduction number $R_{0}$ in terms of model parameters. Our results indicate that treatment of at-risk population groups, improving sanitation, hygiene education, and snail control are effective measures in controlling human schistosomiasis in these lakes and marshland regions.

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