Research article

Multiple infection leads to backward bifurcation for a schistosomiasis model

  • 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.

    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

    Related Papers:

  • 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.


    加载中


    [1] T. Britton, T. House, A.L. Lloyd, D. Mollison, S. Riley and P. Trapma, Five challenges for stochastic epidemic models involving global transmission, Epidemics, 10 (2015), 54–57.
    [2] Department of disease control of the ministry of health of the people's republic of China, Handbook of schistosomiasis control, Shanghai Science and Technology Press, 2000. (In Chinese)
    [3] O. Diekmann, J.A.P. Heesterbeek and J.A.J. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol.,28 (1990), 365–382.
    [4] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.
    [5] Z.L. Feng, C.C. Li and F.A. Milner, Schistosomiasis models with density dependence and age of infection in snail dynamics, Math. Biosci., 177 (2002), 271–286.
    [6] Z.L. Feng, A. Eppert, F.A. Milner and D.J. Minchella, Estimation of parameters governing the transmission dynamics of schistosomes, Appl. Math. Lett., 17 (2004), 1105–1112.
    [7] Z.L. Feng, C.C. Li and F.A. Milner, Schistosomiasis models with two migrating human groups, Math. Comput. Model., 41 (2005), 1213–1230.
    [8] S.J. Gao, Y.Y. He and Y.J. Liu, Field transmission intensity of Schistosoma japonicum measured by basic reproduction ratio from modified Barbours model, Paras. Vector., 6 (2013), 1–10.
    [9] J.H. Ge, S.Q. Zhang and T.P.Wang, Efects of flood On the prevalence of schistosomiasis in Anhui province in 1998, J. Trop. Dis. Parasitol., 2 (2004), 131–134. (In Chinese)
    [10] J.C. Kamgang and G. Sallet, Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium(DFE), Math. Biosci., 213 (2008), 1–12.
    [11] T. Leenstra, H.M. Coutinho, L.P. Acosta, G.C. Langdonet, L. Su, R.M. Olveda, S.T. McGarvey, J.D. Kurtis and J.F. Friedman, Schistosoma japonicum reinfection after Praziquantel treatment causes anemia associated with inflammation, Infect. Immun., 74 (2006), 6398–6407.
    [12] S.B. Mao, Biology of schistosome and control of schistosomiasis, People's Health Press, 1990. (In Chinese)
    [13] L.X. Qi, J.A. Cui, Y. Gao and H.P. Zhu, Modeling the schistosomiasis on the islets in Nanjing, Int. J. Biomath., 5 (2012), 1–17.
    [14] L.X. Qi and J.A. Cui, Mathematical Model of Schistosomiasis under Flood in Anhui Province, Abstr. Appl. Anal., 2014 (2014), 1–7.
    [15] S. Riley, H. Carabin, P. Blisle, L. Josephet, V. Tallo, E. Balolong, A.L.Willingham, T.J. Fernandez, R.O. Gonzales, R. Olveda and S.T. McGarvey, Multi-host transmission dynamics of schistosoma japonicum in Samar province, the Philippines, PLoS Med., 5 (2008), 70–78.
    [16] WHO, Schistosomiasis, http://www.who.int/mediacentre/factsheets/fs115/en/
    [17] H.J. Xu, X.L. Fu, J.X. Chen, C.M. Xia and J.B. Qiu, Immunopathological observations on the infection of Schistosoma japonicum induced by di erent manners, Chin. J. Zoonoses, 22 (2006), 647–650.
    [18] S.Q. Zhang, F.H. Gao, G.H. Zhang, H. Wang and T.P. Wang, Trend analysis of schistosomiasis endemic situation in Anhui Province from 2004 to 2014, Chin. J. Schisto. Control, 27 (2015), 235–240.
    [19] G.M. Zhao and J.X. Liu, Study the disease index of schistosoma japonicum infection in the lake region, Chin. J. Schisto. Control, 13 (2001), 173–175. (In Chinese)
    [20] L. Zou and S.G. Ruan, Schistosomiasis transmission and control in China, Acta Trop., 143 (2015), 51–57.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3012) PDF downloads(632) Cited by(2)

Article outline

Figures and Tables

Figures(4)  /  Tables(1)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog