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Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis

Author

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  • Ebrima Kanyi
  • Ayodeji Sunday Afolabi
  • Nelson Owuor Onyango

Abstract

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 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.

Suggested Citation

  • Ebrima Kanyi & Ayodeji Sunday Afolabi & Nelson Owuor Onyango, 2021. "Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnljam:v:2021:y:2021:i:1:n:6653796
    DOI: 10.1155/2021/6653796
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    References listed on IDEAS

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    1. Abidemi, A. & Abd Aziz, M.I. & Ahmad, R., 2020. "Vaccination and vector control effect on dengue virus transmission dynamics: Modelling and simulation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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    Cited by:

    1. Timothy Kamara & Michael Byamukama & Martin Karuhanga, 2022. "Modelling the Role of Treatment, Public Health Education, and Chemical Control Strategies on Transmission Dynamics of Schistosomiasis," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Habtamu Ayalew Engida, 2025. "Analysis of a Comprehensive Mathematical Model for Leptospirosis Dynamics: An Optimal Control Application," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    3. Habtamu Ayalew Engida & David Mwangi Theuri & Duncan Kioi Gathungu & John Gachohi & Haileyesus Tessema Alemneh, 2025. "A Coinfection Model of Leptospirosis and Melioidosis With Optimal Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    4. Dagnaw Tantie Yihunie & Joseph Y. T. Mugisha & Dawit Melese Gebru & Haileyesus Tessema Alemneh, 2024. "Modeling and Analysis of Fasciola Hepatica Disease Transmission," Abstract and Applied Analysis, John Wiley & Sons, vol. 2024(1).

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