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Analysis of a hand–foot–mouth disease model

Swarnali Sharma

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711 103, India

E-mail Address: swarnali.sharma87@gmail.com

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and

G. P. Samanta

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711 103, India

E-mail Address: g_p_samanta@yahoo.co.uk

E-mail Address: gpsamanta@math.iiests.ac.in

Corresponding author.

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https://doi.org/10.1142/S1793524517500164Cited by:19 (Source: Crossref)

Abstract

In this paper, we have introduced a six-compartmental epidemic model with hand, foot and mouth disease (HFMD) infection. The total population is divided into six subclasses, namely susceptible, exposed, infective in asymptomatic phase, infective in symptomatic phase, quarantined and recovered class. Some basic properties such as boundedness and non-negativity of solutions are discussed. The basic reproduction number ( $R_{0}$ ) of the system is obtained using next generation matrix method. Then the deterministic dynamical behaviors of the system are studied. Our study includes the existence and stability analysis of equilibrium points of the system. The sensitivity analysis of our system helps us to find out the parameters of greater interest. Next, we deal with the epidemic model with three controls (two treatment controls with quarantine control). We show that there exists an optimal control, which is effective in controlling the disease outbreak in a cost effective way. Numerical simulation is presented with the help of MATLAB, which shows the reliability of our model from the practical point of view.

Keywords:

AMSC: 92B05, 92D25, 92D30

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