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Stability and Hopf Bifurcation of Within-Host
Chikungunya Virus Infection Model
Muhammad Salehin Bin Mat Said @ Abdul Rahman
Supervisor: Assoc. Prof. Dr. Zabidin Bin Salleh
Bachelor of Science (Financial Mathematics)
School of Informatics and Applied Mathematics
Chikungunya virus is an arthropod-borne alphavirus which is transmitted by mosquitoes.
Hopf bifurcation is basically a critical point where a system’s stability switch and a periodic
solution arises. In other words, it is local bifurcation in which a fixed point of dynamic
system loses stability. In this research, we will study the stability and also the hopf
bifurcation of Chikungunya virus infection model. Now we consider finding the stability of
equilibria in the virus infection model, the existence of Hopf bifurcation inside the model
also the stability and direction of the Chikungunya virus infection model. We consider
using the Jacobian Matrix method in finding the stability of equilibria in the model, and
using the Normal Form method and Centre Manifold Theorem to find the stability and
direction of Hopf Bifurcation inside the model. The result of this research are, the model
has asymptotically stable equilibria, there is an existence of Hopf bifurcation and it is
asymptotically stable with supercritical direction.
830 | UMT UNDERGRADUATE RESEARCH DAY 2018