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Mathematical Analysis of an Anthroponotic Cutaneous Leishmaniasis Model with Asymptomatic Infection

Author

Listed:
  • Muntaser Safan

    (Department of Mathematical Science, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia)

  • Alhanouf Altheyabi

    (Department of Mathematical Science, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia
    Department of Mathematics, Faculty of Sciences, Taif University, Taif 21944, Saudi Arabia)

Abstract

This work aims mainly to study the impact of experiencing asymptomatic anthroponotic cutaneous leishmaniasis (ACL) infection on the overall dynamics and outcomes of the disease. Therefore, a deterministic model for the transmission dynamics of ACL of type SEAIS in the human host and SI in sandfly populations is proposed and mathematically analyzed. The model is shown to be well-posed. Its equilibrium and stability analyses are shown. The equilibrium analysis shows that the model has an ACL-free equilibrium that is proven to be locally and globally asymptotically stable if and only if R 0 < 1 . In addition, the model has a unique ACL-endemic equilibrium that is shown to exist and be locally asymptotically stable if and only if R 0 > 1 . Numerical simulations are performed to show the asymptotic stability of these equilibriums. In addition, the effect of ignoring asymptomatic infections is studied and the analysis shows that ignoring the development of asymptomatic infections overestimates the effort required to eliminate the infection. Moreover, it implies inaccurate measures of controlling ACL infection, especially those based on either using insecticide sprays or bednets.

Suggested Citation

  • Muntaser Safan & Alhanouf Altheyabi, 2023. "Mathematical Analysis of an Anthroponotic Cutaneous Leishmaniasis Model with Asymptomatic Infection," Mathematics, MDPI, vol. 11(10), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2388-:d:1152080
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    References listed on IDEAS

    as
    1. Bi, Kaiming & Chen, Yuyang & Zhao, Songnian & Ben-Arieh, David & (John) Wu, Chih-Hang, 2020. "A new zoonotic visceral leishmaniasis dynamic transmission model with age-structure," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Muhammad Zamir & Gul Zaman & Ali Saleh Alshomrani, 2016. "Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-19, August.
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