A realistic model for the periodic dynamics of the hand-foot-and-mouth disease

I. A. Moneim; G. A. Mosa; I. A. Moneim; G. A. Mosa

doi:10.3934/math.2022145

AIMS Mathematics

2022, Volume 7, Issue 2: 2585-2601. doi: 10.3934/math.2022145

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Research article

A realistic model for the periodic dynamics of the hand-foot-and-mouth disease

I. A. Moneim ,
G. A. Mosa ^,

Department of Mathematics, Faculty of Science, Benha University, Egypt

Received: 23 August 2021 Accepted: 10 November 2021 Published: 17 November 2021
MSC : 93A30, 97Mxx

In this paper, an SEIQRS model with a periodic vaccination strategy is studied for the dynamics of the Hand-Foot-and-Mouth Disease (HFMD). This model incorporates a seasonal variation in the disease transmission rate $ \beta (t) $. Our model has a unique disease free periodic solution (DFPS). The basic reproductive number $ R_{0} $ and its lower and upper bounds, $ R_{0}^{inf} $ and $ R_{0}^{sup} $ respectively, are defined. We show that the DFPS is globally asymptotically stable when $ R_{0}^{sup} < 1 $ and unstable if $ R_{0}^{inf} > 1 $. Computer simulations of our model have been conducted using a novel periodic function of the contact rate. This novel function imitates the seasonality in the observed, multi-peaks pattern, data. Clear and good matching between real data and the obtained simulation results are shown. The obtained simulation results give a good prediction and possible control of the disease dynamics.
- modelling,
- simulation,
- global stability,
- periodicity,
- HFMD,
- $ R_0 $
Citation: I. A. Moneim, G. A. Mosa. A realistic model for the periodic dynamics of the hand-foot-and-mouth disease[J]. AIMS Mathematics, 2022, 7(2): 2585-2601. doi: 10.3934/math.2022145

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Abstract

In this paper, an SEIQRS model with a periodic vaccination strategy is studied for the dynamics of the Hand-Foot-and-Mouth Disease (HFMD). This model incorporates a seasonal variation in the disease transmission rate $ \beta (t) $. Our model has a unique disease free periodic solution (DFPS). The basic reproductive number $ R_{0} $ and its lower and upper bounds, $ R_{0}^{inf} $ and $ R_{0}^{sup} $ respectively, are defined. We show that the DFPS is globally asymptotically stable when $ R_{0}^{sup} < 1 $ and unstable if $ R_{0}^{inf} > 1 $. Computer simulations of our model have been conducted using a novel periodic function of the contact rate. This novel function imitates the seasonality in the observed, multi-peaks pattern, data. Clear and good matching between real data and the obtained simulation results are shown. The obtained simulation results give a good prediction and possible control of the disease dynamics.

References

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