Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate

Alsahafi, S; Woodcock, S

Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate

Alsahafi, S Woodcock, S

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Publisher:: MDPI AG
Publication Type:: Journal Article
Citation:: Mathematics, 9, (18), pp. 2186-2186

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Field	Value	Language
dc.contributor.author	Alsahafi, S
dc.contributor.author	Woodcock, S https://orcid.org/0000-0003-4903-3164
dc.date.accessioned	2021-09-08T08:52:29Z
dc.date.available	2021-09-08T08:52:29Z
dc.identifier.citation	Mathematics, 9, (18), pp. 2186-2186
dc.identifier.issn	2227-7390
dc.identifier.uri	http://hdl.handle.net/10453/150402
dc.description.abstract	<jats:p>In this article, we examine the dynamics of a Chikungunya virus (CHIKV) infection model with two routes of infection. The model uses four categories, namely, uninfected cells, infected cells, the CHIKV virus, and antibodies. The equilibrium points of the model, which consist of the free point for the CHIKV and CHIKV endemic point, are first analytically determined. Next, the local stability of the equilibrium points is studied, based on the basic reproduction number (R0) obtained by the next-generation matrix. From the analysis, it is found that the disease-free point is locally asymptotically stable if R0≤1, and the CHIKV endemic point is locally asymptotically stable if R0>1. Using the Lyapunov method, the global stability analysis of the steady-states confirms the local stability results. We then describe our design of an optimal recruitment strategy to minimize the number of infected cells, as well as a nonlinear optimal control problem. Some numerical simulations are provided to visualize the analytical results obtained.</jats:p>
dc.language	en
dc.publisher	MDPI AG
dc.relation.ispartof	Mathematics
dc.relation.isbasedon	10.3390/math9182186
dc.rights	info:eu-repo/semantics/openAccess
dc.title	Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate
dc.type	Journal Article
utslib.citation.volume	9
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access	*
dc.date.updated	2021-09-08T08:52:29Z
pubs.issue	18
pubs.publication-status	Published online
pubs.volume	9
utslib.citation.issue	18

Abstract:

In this article, we examine the dynamics of a Chikungunya virus (CHIKV) infection model with two routes of infection. The model uses four categories, namely, uninfected cells, infected cells, the CHIKV virus, and antibodies. The equilibrium points of the model, which consist of the free point for the CHIKV and CHIKV endemic point, are first analytically determined. Next, the local stability of the equilibrium points is studied, based on the basic reproduction number (R0) obtained by the next-generation matrix. From the analysis, it is found that the disease-free point is locally asymptotically stable if R0≤1, and the CHIKV endemic point is locally asymptotically stable if R0>1. Using the Lyapunov method, the global stability analysis of the steady-states confirms the local stability results. We then describe our design of an optimal recruitment strategy to minimize the number of infected cells, as well as a nonlinear optimal control problem. Some numerical simulations are provided to visualize the analytical results obtained.

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http://hdl.handle.net/10453/150402