Multiple infection leads to backward bifurcation for a schistosomiasis model

Longxing Qi; Shoujing Tian; Jing-an Cui; Tianping Wang; Longxing Qi; Shoujing Tian; Jing-an Cui; Tianping Wang

doi:10.3934/mbe.2019033

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 2: 701-712. doi: 10.3934/mbe.2019033

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Research article

Multiple infection leads to backward bifurcation for a schistosomiasis model

1.
School of Mathematical Sciences, Anhui University, Hefei, 230601, P.R.China
2.
College of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
3.
Anhui Institute of Schistosomiasis, Hefei, 230061, P.R.China

Received: 19 March 2017 Accepted: 02 November 2018 Published: 15 January 2019

Based on years of experience in schistosomiasis prevention and treatment, one of the typical features of schistosomiasis is multiple infection of a human host by parasites, which may dramatically a ect the host's infectivity. In this paper we establish a schistosomiasis model that takes into consideration multiple infection by separating humans with single and multiple infectious. The disease free equilibrium is shown to be globally asymptotically stable under certain condition. The model analysis suggests that a backward bifurcation may occur if the transmission rate from multiple infected humans to snails is high. This conclusion has not been seen in previous models of schistosomiasis. Such backward bifurcation is not possible without considering multiple infections. This conclusion may provide a new threshold theory for the prevention and treatment of schistosomiasis. Furthermore, numerical simulations suggest that e ective treatment of humans with multiple infection is important to control schistosomiasis. Especially, prevention of multiple infection may be critical.
- schistosomiasis model,
- multiple infection,
- backward bifurcation
Citation: Longxing Qi, Shoujing Tian, Jing-an Cui, Tianping Wang. Multiple infection leads to backward bifurcation for a schistosomiasis model[J]. Mathematical Biosciences and Engineering, 2019, 16(2): 701-712. doi: 10.3934/mbe.2019033

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Abstract

Based on years of experience in schistosomiasis prevention and treatment, one of the typical features of schistosomiasis is multiple infection of a human host by parasites, which may dramatically a ect the host's infectivity. In this paper we establish a schistosomiasis model that takes into consideration multiple infection by separating humans with single and multiple infectious. The disease free equilibrium is shown to be globally asymptotically stable under certain condition. The model analysis suggests that a backward bifurcation may occur if the transmission rate from multiple infected humans to snails is high. This conclusion has not been seen in previous models of schistosomiasis. Such backward bifurcation is not possible without considering multiple infections. This conclusion may provide a new threshold theory for the prevention and treatment of schistosomiasis. Furthermore, numerical simulations suggest that e ective treatment of humans with multiple infection is important to control schistosomiasis. Especially, prevention of multiple infection may be critical.

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