An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors

Fatima Sulayman, Farah Aini Abdullah and Mohd Hafiz Mohd
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Fatima Sulayman: School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia
Farah Aini Abdullah: School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia
Mohd Hafiz Mohd: School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia

Mathematics, 2021, vol. 9, issue 4, 1-23

Abstract: This study extends a deterministic mathematical model for the dynamics of tuberculosis transmission to examine the impact of an imperfect vaccine and other exogenous factors, such as re-infection among treated individuals and exogenous re-infection. The qualitative behaviors of the model are investigated, covering many distinct aspects of the transmission of the disease. The proposed model is observed to show a backward bifurcation, even when R v < 1 . As such, we assume that diminishing R v to less than unity is not effective for the elimination of tuberculosis. Furthermore, the results reveal that an imperfect tuberculosis vaccine is always effective at reducing the spread of infectious diseases within the population, though the general effect increases with the increase in effectiveness and coverage. In particular, it is shown that a limited portion of people being vaccinated at steady-state and vaccine efficacy assume a equivalent role in decreasing disease burden. From the numerical simulation, it is shown that using an imperfect vaccine lead to effective control of tuberculosis in a population, provided that the efficacy of the vaccine and its coverage are reasonably high.

Keywords: tuberculosis model; vaccination; effective reproduction number; stability analysis; bifurcation analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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