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A Human-Bovine Schistosomiasis Mathematical Model with Treatment and Mollusciciding

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Abstract

To mitigate the spread of schistosomiasis, a deterministic human-bovine mathematical model of its transmission dynamics accounting for contaminated water reservoirs, including treatment of bovines and humans and mollusciciding is formulated and theoretically analyzed. The disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number \(R_0<1\), while global stability of the endemic equilibrium is investigated by constructing a suitable Lyapunov function. To support the analytical results, parameter values from published literature are used for numerical simulations and where applicable, uncertainty analysis on the non-dimensional system parameters is performed using the Latin Hypercube Sampling and Partial Rank Correlation Coefficient techniques. Sensitivity analysis to determine the relative importance of model parameters to disease transmission shows that the environment-related parameters namely, \(\varepsilon _s\) (snails shedding rate of cercariae), \(p_s\) (probability that cercariae shed by snails survive), c (fraction of the contaminated environment sprayed by molluscicides) and \(\mu _c\) (mortality rate of cercariae) are the most significant to mitigate the spread of schistosomiasis. Mollusciciding, which directly impacts the contaminated environment as a single control strategy is more effective compared to treatment. However, concurrently applying mollusciciding and treatment will yield a better outcome.

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Acknowledgements

S. Kadaleka thanks the University of Malawi (Malawi Polytechnic) for financial support. The authors acknowledge support of the School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, in the production of this manuscript. The authors are grateful to the anonymous reviewers for their constructive comments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Malawi, Chichiri, Blantyre, Malawi

    Solomon Kadaleka

  2. School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa

    Solomon Kadaleka, Shirley Abelman & Jean M. Tchuenche

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  1. Solomon Kadaleka
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Correspondence to Shirley Abelman.

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Kadaleka, S., Abelman, S. & Tchuenche, J.M. A Human-Bovine Schistosomiasis Mathematical Model with Treatment and Mollusciciding. Acta Biotheor 69, 511–541 (2021). https://doi.org/10.1007/s10441-021-09416-0

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