2021 Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis
Ebrima Kanyi, Ayodeji Sunday Afolabi, Nelson Owuor Onyango
Author Affiliations +
J. Appl. Math. 2021: 1-20 (2021). DOI: 10.1155/2021/6653796


This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R0, is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R0>1. It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R0<1, and the unique endemic equilibrium point is locally asymptotically stable whenever R0>1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R0=1, the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis.


This research work is supported by the Pan African University through its scholarship program.


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Ebrima Kanyi. Ayodeji Sunday Afolabi. Nelson Owuor Onyango. "Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis." J. Appl. Math. 2021 1 - 20, 2021. https://doi.org/10.1155/2021/6653796


Received: 23 February 2021; Accepted: 23 April 2021; Published: 2021
First available in Project Euclid: 28 July 2021

Digital Object Identifier: 10.1155/2021/6653796

Rights: Copyright © 2021 Hindawi


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