Dynamics of a SVEIR Epidemic Model with a Delay in Diagnosis in a Changing Environment

Authors

  • Hamadoum Dicko Laboratory of Mathematics, Computer Science and Applications, University Norbert ZONGO, BP 376 Koudougou, Burkina Faso https://orcid.org/0009-0006-0153-9042
  • Ali Traoré Mathematics and Computer Science Laboratory, University Joseph Ki-Zerbo, BP 7021, Ouagadougou 03, Burkina Faso https://orcid.org/0000-0001-6647-7985
  • Désiré Ouedraogo Mathematics and Computer Science Laboratory, University Joseph Ki-Zerbo, BP 7021, Ouagadougou 03, Burkina Faso https://orcid.org/0009-0001-7514-3052

DOI:

https://doi.org/10.37256/cm.5320244865

Keywords:

sensitivity, delays in diagnosis, changing environment, Lyapunov function

Abstract

A SVEIR epidemic model with a delay in diagnosis is studied in a constant and variable environment. The mathematical analysis shows that the dynamics of the model in the constant environment are completely determined by the magnitude of the delay-induced reproduction number mceclip1-e7c3748072ac5fa6e47aa8bf7e3f8a51.png. We established that if mceclip2-ec2436cbe7d3552df7ed3e841cdee9b6.png < 1, the disease-free equilibrium is globally asymptotically stable, and when mceclip3-220272d21904f66eac6f39f3a008d1dd.png > 1 the endemic equilibrium is globally asymptotically stable. In the variable environment, the model undergoes a transcritical bifurcation for mceclip4-c8156368ba219ab492f7d623a0b04c02.png= 1 leading to changes in the stability of the equilibrium points. The analytical effect of the delays in epidemic diagnosis is investigated. A minimum diagnosis rate αmin has been determined to face or control the disease effectively. Finally, numerical illustrations were presented to support the theoretical results.

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Published

2024-09-09

How to Cite

1.
Dicko H, Traoré A, Ouedraogo D. Dynamics of a SVEIR Epidemic Model with a Delay in Diagnosis in a Changing Environment. Contemp. Math. [Internet]. 2024 Sep. 9 [cited 2024 Dec. 22];5(3):3762-89. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/4865