Analysis and optimal control of a deterministic Zika virus model

Volume 15, Issue 2, pp 88--108 http://dx.doi.org/10.22436/jnsa.015.02.02

Publication Date: August 20, 2021 Submission Date: April 27, 2021 Revision Date: May 17, 2021 Accteptance Date: July 05, 2021

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Authors

D. Denu - Department of Mathematics, Georgia Southern University, 11935 Abercorn Street, Savannah, GA 31419, USA. H. Son - Mathematics, Division of Science, Southern Wesleyan University, 907 Wesleyan Drive, Central, SC 29630, USA.

Abstract

In this paper, we consider a deterministic model explaining how Zika virus is transmitted between human and mosquito. The human population is divided into three groups as susceptible \((x_1)\), infected \((x_2)\), and treated \((x_3)\). Similarly, the mosquito population is divided into susceptible \((y_1)\) and infected \((y_2)\) groups. First, we conduct the local and global stability of the disease-free and endemic equilibrium points in relation to the basic reproductive number. We also study the sensitivity of the basic reproductive number and the endemic equilibrium point with respect to each parameters used in the model. Furthermore, we apply optimal control theory to show that there are cost effective control methods with the prevention effort \((u_1)\) of the contact between human and vector and the effort of treatment \((u_2)\) for human. Finally, we provide numerical simulations to support and illustrate some of the theoretical results.

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Keywords

• Deterministic Zika virus model
• basic reproductive number
• local and global stability
• sensitivity analysis
• optimal control

MSC

•  92D30
•  49Q12

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