DOI: https://doi.org/10.14710/jfma.v7i2.21608

ANALYSIS OF A NON LINEAR DYNAMICS MODEL FOR TRANSMISSION TUBERCULOSIS IN NIGERIA INCORPORATING TREATMENT AND VACCINATION

*Olusegun Joseph Fenuga orcid  -  Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria, Nigeria
Adubi Olaoluwa Yusuff  -  Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria, Nigeria
Adubi Olaoluwa Yusuff  -  Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria, Nigeria
Nura Isah  -  Department of Mathematics, Faculty of Physical and Computing Sciences, Usmanu Danfodiyo University, Sokoto, Nigeria, Nigeria
Nura Isah  -  Department of Mathematics, Faculty of Physical and Computing Sciences, Usmanu Danfodiyo University, Sokoto, Nigeria, Nigeria

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Abstract

This work models and analyzes the transmission of tuberculosis infection with the impact of vaccination and treatment on the bacteria in Nigeria from 2010 to 2022 incorporating treatment and vaccination. The susceptible-vaccinated-Exposed-Infected-Recovered (SVEIR) model is used for the transmission of the bacteria in which the with immigrants are exposed to infection infectious individuals, and it is assumed that there is permanent immunity and homogenous mixing against the bacteria. The constant immigration of the infected individuals into the population makes it impossible for the disease to die out and so there is no disease-free equilibrium. The fraction of chemoprophylaxis Bacillus Calmette-Guerin (BCG) was incorporated into the model equation for successful vaccination. Stability analysis shows that a disease free equilibrum is locally asymptotically stable for R0<1 and endemic equilibrum which is stable for R0>1 which can wipe out the whole population. Hence, treatment and vaccination are the measures that can reduce below 1 in order to control tuberculosis.

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Keywords: Population, Tuberculosis, Transmission, Vaccination, Free equilibrum, Susceptible, Latent and infectious.

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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