Mathematical Analysis and Simulation of an Age-Structured Model with Two-Patch and an Uncontrolled Migration: Application to Tuberculosis

Authors

  • Abdoul Wahid Badjo Kimba
  • Dijbo Moustapha Dosso University
  • Bisso Saley

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i4.4556

Keywords:

age-structured, reproductive number, two-patch, tuberculosis, stability, migration, simulation, uncontrolled, endemic.

Abstract

In this paper, we studied a two-patch age-structured model of tuberculosis in a context where the migration is not controlled. Motivated by the fact that no author has highlighted the impact of migration on the dynamics of transmission of tuberculosis. Each subpopulation is subdivided into five compartments: susceptible; latent, vaccinated, infective and treated. After the determination of the reproductive numbers R(ψ, ρ) and R0(ρ), we established the conditions of the global and local stability of the equilibrium point without disease. It has been shown that there is only one point of endemic equilibrium. Numerical simulations show that uncontrolled migration negatively influences the dynamics of tuberculosis.

Author Biography

Dijbo Moustapha, Dosso University

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How to Cite

Badjo Kimba, A. W., Moustapha, D., & Saley, B. (2022). Mathematical Analysis and Simulation of an Age-Structured Model with Two-Patch and an Uncontrolled Migration: Application to Tuberculosis. European Journal of Pure and Applied Mathematics, 15(4), 2054–2073. https://doi.org/10.29020/nybg.ejpam.v15i4.4556