Lyapunov Functions and Qualitative Analysis of an Epidemic Model with Vaccination

Authors

  • Md Saiful Islam Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman University, Kishoreganj, Bangladesh
  • Kazi Mehedi Mohammad 2Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
  • Md Mashih Ibn Yasin Adan Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman University, Kishoreganj, Bangladesh
  • Md Kamrujjaman Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh

DOI:

https://doi.org/10.3329/ganit.v44i1.71859

Keywords:

Lyapunov functions; LaSalle’s invariance; global stability; uniform persistence; vaccination.

Abstract

The spatial-temporal diffusion dynamics of infectious disease with vaccination therapy are studied through a mathematical model. We have investigated the well-posedness, disease-free equilibrium, disease equilibrium, the existence and the uniqueness of solutions, and the calculation of basic reproduction numbers by Jacobian matrix. After that, the positivity, as well as boundedness of solutions, are also established. The global stability of diseasefree and steady-state disease results is established by utilizing compatible Lyapunov functions and LaSalle’s invariance principle. Illustration of the numerical examples to show the dynamics of different population groups over time. The effects of different parameters on the compartments are shown in detail.

GANIT J. Bangladesh Math. Soc. 44.1 (2024) 01- 22

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Published

2024-03-14

How to Cite

Islam, M. S. ., Mohammad, K. M., Yasin Adan, M. M. I. ., & Kamrujjaman , M. (2024). Lyapunov Functions and Qualitative Analysis of an Epidemic Model with Vaccination. GANIT: Journal of Bangladesh Mathematical Society, 44(1), 1–22. https://doi.org/10.3329/ganit.v44i1.71859

Issue

Vol. 44 No. 1 (2024)

Section

Articles

License

The copyright of GANIT: Journal of Bangladesh Mathematical Society is reserved by Bangladesh Mathematical Society (web: https://bdmathsociety.org/)