Backward Bifurcation and Hysteresis in a Mathematical Model of COVID19 with Imperfect Vaccine

Authors

  • Solomon Isa Rwat School of Mathematical Sciences, Universiti Sians Malaysia
  • Noor Atinah Ahmad School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Minden, Pulau Pinang, Malaysia

DOI:

https://doi.org/10.11113/matematika.v39.n1.1458

Abstract

Vaccination has been used as strategy to eradicate the spread of COVID-19. But imperfect vaccine has been reported to induce backward bifurcation and hysteresis in mathematical models of disease transmission. Backward bifurcation is a phenomenon whereby a stable endemic equilibrium exists contemporaneously with a stable disease-free equilibrium when the basic reproduction number is less than 1. This situation can cause difficulty in controlling an epidemic because the basic reproduction is no longer the only means of eradicating the disease. In this paper, we propose a mathematical model for the transmission of disease which includes imperfect vaccination. We show that our model is capable of capturing backward bifurcation under certain conditions. By using parameters that are relevant to COVID-19 transmission in Malaysia, our numerical analysis shows that low vaccine efficacy can trigger backward bifurcation.

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Published

15-04-2023

How to Cite

Rwat, S. I., & Ahmad, N. A. A. (2023). Backward Bifurcation and Hysteresis in a Mathematical Model of COVID19 with Imperfect Vaccine. MATEMATIKA, 39(1), 87–99. https://doi.org/10.11113/matematika.v39.n1.1458

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Articles