# Numerical solution and stability analysis of a childhood-disease model with vaccination and relapse

Article

Rabiu, Musa, Adeniji, Saidat Morenike and Jimoh, Folashade Mistura. 2020. "Numerical solution and stability analysis of a childhood-disease model with vaccination and relapse." Applied Mathematics E-Notes. 20, pp. 499-515.
Article Title Numerical solution and stability analysis of a childhood-disease model with vaccination and relapse 41462 Article Rabiu, Musa, Adeniji, Saidat Morenike and Jimoh, Folashade Mistura Applied Mathematics E-Notes 20, pp. 499-515 17 2020 Tsinghua University Press Taiwan 1607-2510 https://www.math.nthu.edu.tw/~amen/ In this research, a childhood disease model that incorporates relapse and vaccination was developed and systematically analyzed using sets of non-linear Ordinary Di§erential Equations. The model exhibits disease-free equilibrium which is locally and globally asymptotically stable whenever the threshold parameter Ro is less than unity and unstable otherwise. It also exhibits endemic equilibrium which was proved to be locally asymptotically stable whenever Ro is greater than unity. The model was then modiÖed to include vaccination programme capable of reducing disease burden. The global stability analysis of the endemic equilibrium points was carried out using geometric and compound matrix approach satisfying the Bendixon criterion when Rv > 1. The numerical solution of the model was performed using Adams method coded in Python Programming Language to explore the biological implication of force of infection, vaccination and relapse. The result shows that for the disease to be eradicated, the vaccination rate f must be robust, relapse rate  reduced and the contact rate among children should be avoided or minimized. Mathematical modelling Does not contain sensitive content 401706. Numerical modelling and mechanical characterisation Files associated with this item cannot be displayed due to copyright restrictions. University of KwaZulu-Natal, South Africa University of Ilorin, Nigeria Alhikmah University, Nigeria

https://research.usq.edu.au/item/z20vw/numerical-solution-and-stability-analysis-of-a-childhood-disease-model-with-vaccination-and-relapse

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