Analysis of an SQEIAR epidemic model with media coverage and asymptomatic infection

Xiangyun Shi; Xiwen Gao; Xueyong Zhou; Yongfeng Li; Xiangyun Shi; Xiwen Gao; Xueyong Zhou; Yongfeng Li

doi:10.3934/math.2021712

AIMS Mathematics

2021, Volume 6, Issue 11: 12298-12320. doi: 10.3934/math.2021712

Previous Article Next Article

Research article Special Issues

Analysis of an SQEIAR epidemic model with media coverage and asymptomatic infection

1.
School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, Henan, China
2.
Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, Henan, China

Received: 18 June 2021 Accepted: 11 August 2021 Published: 26 August 2021
MSC : 92D30

An SQEIAR model with media coverage and asymptomatic infection is proposed for populations with a certain level of immunity. Firstly, we discuss the extinction and persistence for the diseases of the model by using basic reproduction number $ \mathcal{R}_C $. Then the parameter threshold is analyzed and the effect of parameters on the basic reproduction number is discussed. Furthermore, the optimal media coverage strategy and quarantine strategy for optimal problems under quadratic cost function are derived by applying Pontryagin's Maximum Principle.
- epidemic model,
- media coverage,
- asymptomatic infection,
- optimal control theory
Citation: Xiangyun Shi, Xiwen Gao, Xueyong Zhou, Yongfeng Li. Analysis of an SQEIAR epidemic model with media coverage and asymptomatic infection[J]. AIMS Mathematics, 2021, 6(11): 12298-12320. doi: 10.3934/math.2021712

Related Papers:

Abstract

An SQEIAR model with media coverage and asymptomatic infection is proposed for populations with a certain level of immunity. Firstly, we discuss the extinction and persistence for the diseases of the model by using basic reproduction number $ \mathcal{R}_C $. Then the parameter threshold is analyzed and the effect of parameters on the basic reproduction number is discussed. Furthermore, the optimal media coverage strategy and quarantine strategy for optimal problems under quadratic cost function are derived by applying Pontryagin's Maximum Principle.

References

[1]	K. Tharakaraman, A. Jayaraman, R. Raman, K. Viswanathan, N. Stebbins, D. Johnson, et al., Glycan receptor binding of the influenza a virus H7N9 hemagglutinin, Cell, 153 (2013), 1486-1493. doi: 10.1016/j.cell.2013.05.034
[2]	K. Tharakaraman, R. Raman, K. Viswanathan, N. Stebbins, A. Jayaraman, A. Krishnan, et al., Structural determinants for naturally evolving H5N1 hemagglutinin to switch its receptor specificity, Cell, 153 (2013), 1475-1485. doi: 10.1016/j.cell.2013.05.035
[3]	W. D. Wang, S. G. Ruan, Simulating the SARS outbreak in Beijingwith limited data, J. Theoret. Biol., 227 (2004), 369-379. doi: 10.1016/j.jtbi.2003.11.014
[4]	X. F. Yan, Y. Zou, Optimal and sub-optimal quarantine and isolation control in SARS epidemics, Math. Comput. Model., 47 (2008), 235-245. doi: 10.1016/j.mcm.2007.04.003
[5]	J. X. Guan, Y. Y. Wei, Y. Zhao, F. Chen, Modeling the transmission dynamics of COVID-19 epidemic: A systematic review, J. Biomed. Res., 34 (2020), 422-430. doi: 10.7555/JBR.34.20200119
[6]	X. M. Rong, L. Yang, H. D. Chu, M. Fan, Effect of delay in diagnosis on transmission of COVID-19, Math. Biosci. Eng., 17 (2020), 2725-2740. doi: 10.3934/mbe.2020149
[7]	B. Tang, X. Wang, Q. Li, N. L. Bragazzi, S. Y. Tang, Y. N. Xiao, et al., Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions, J. Clin. Med., 9 (2020), 462. doi: 10.3390/jcm9020462
[8]	Rahim ud Din, Aly R. Seadawy, Kamal Shah, Aman Ullah, Dumitru Baleanu, Study of global dynamics of COVID-19 via a new mathematical model, Results Phys., 19 (2020), 103468. doi: 10.1016/j.rinp.2020.103468
[9]	C. Sun, W. Yang, J. Arino, K. Khan, Effect of media-induced social distancing on disease transmission in a two patch setting, Math. Biosci., 230 (2011), 87-95. doi: 10.1016/j.mbs.2011.01.005
[10]	I. F. Mello, L. Squillante, G. O. Gomes, A. C. Seridonio, M. de Souza, Epidemics, the Ising-model and percolation theory: A comprehensive review focused on COVID-19, Physica A, 573 (2021), 125963. doi: 10.1016/j.physa.2021.125963
[11]	H. A. Adekola, I. A. Adekunle, H. O. Egberongbe, S. A. Onitilo, Idris Nasir Abdullahi, Mathematical modeling for infectious viral disease: The COVID-19 perspective, J. Public Aff., 20 (2020), e2306.
[12]	R. Liu, J. Wu, H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases, Comput. Math. Methods Med., 8 (2007), 153-164. doi: 10.1080/17486700701425870
[13]	J. H. Pang, J. A. Cui, An SIRS epidemiological model with nonlinear incidence rate incorporating media coverage, Second International Conference on Information and Computing Science, IEEE, (2009), 116-119.
[14]	J. M. Tchuenche, N. Dube, C. P. Bhunu, R. J. Smith, C. T. Bauch, The impact of media coverage on the transmission dynamics of human influenza, BMC Public Health, 11 (2011), S5.
[15]	A. Wang, Y. Xiao, A Filippov system describing media effects on the spread of infectious diseases, Nonlinear Anal. Hybrid Syst., 11 (2014), 84-97. doi: 10.1016/j.nahs.2013.06.005
[16]	J. Cui, Y. Sun, H. Zhu, The impact of media on the control of infectious diseases, J. Dyn. Differ. Equ., 20 (2007), 31-53.
[17]	Y. P. Liu, J. A. Cui, The impact of media coverage on the dynamics of infectious disease, Int. J. Biomath., 1 (2008), 65-74. doi: 10.1142/S1793524508000023
[18]	P. Shil, Mthematical modeling of viral epidemics: A review, Biomed. Res. J., 3 (2016), 195-215.
[19]	L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko, The mathematical theory of optimal processes, Bell Syst. Tech. J., 27 (1986), 623-656.
[20]	W. H. Fleming, R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, 1975.
[21]	G. P. Sahu, J. Dhar, Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate, Appl. Math. Model., 36 (2012), 908-923. doi: 10.1016/j.apm.2011.07.044
[22]	J. Cui, X. Tao, H. P. Zhu, An SIS infection on model in corporating media coverage, Rocky Mt. J. Math., 38 (2008), 1323-1334.
[23]	G. P. Sahu, J. Dhar, Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity, J. Math. Anal. App., 421 (2015), 1651-1672. doi: 10.1016/j.jmaa.2014.08.019
[24]	G. Birkhoff, G. C. Rota, Ordinary Differential Equations, John Wiley, New York, 1998.
[25]	H. L. Smith, P. Waltman, The Theory of the Chemostat, Cambridge University Press, Cambridge, 1995.
[26]	P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
[27]	C. Castillo-Chavez, B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361-404. doi: 10.3934/mbe.2004.1.361
[28]	C. Castillo-Chavez, Z. L. Feng, W. Huang, On the computation of $\mathcal{R}_0$ and its role on global stability, Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, Springer-Verlag, New York, (2002), 229-250.
[29]	H. I. Freedman, S. Ruan, M. Tang, Uniform persistence and flows near a closed positively invariant set, J. Dynam. Differ. Equ., 6 (1994), 583-600. doi: 10.1007/BF02218848
[30]	M. Safi, A. B. Gumel, Dynamics of a model with quarantine-adjusted incidence and quarantine of susceptible individuals, J. Math. Anal. Appl., 399 (2013), 565-575.
[31]	M. Y. Li, J. R. Graef, L. Wang, Global dynamics of a SEIR model with varying total population size, Math. Biosci., 160 (1999), 191-213. doi: 10.1016/S0025-5564(99)00030-9
[32]	D. L. Lukes, Differential Equations: Classical to Controlled, Mathematics in Science and Engineering, Academic Press, New York, 1982.
[33]	Yaqing Fang, Yiting Nie, Marshare Penny, Transmission dynamics of the COVID-19 outbreak and effectiveness of government interventions: A data-driven analysis, J. Med. Virol., 92 (2020), 645-659. doi: 10.1002/jmv.25750

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)