The influence of an appropriate reporting time and publicity intensity on the spread of infectious diseases

Chang Hou; Qiubao Wang; Chang Hou; Qiubao Wang

doi:10.3934/math.20231199

AIMS Mathematics

2023, Volume 8, Issue 10: 23578-23602. doi: 10.3934/math.20231199

Previous Article Next Article

Research article

The influence of an appropriate reporting time and publicity intensity on the spread of infectious diseases

Chang Hou ,
Qiubao Wang ^,

Department of Mathematical and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

Received: 10 May 2023 Revised: 17 June 2023 Accepted: 30 June 2023 Published: 31 July 2023
MSC : 37H20, 37N25

We present a stochastic time-delay susceptible-exposed-asymptomatic-symptom-vaccinated-recovered (SEAQVR) model with media publicity effect in this study. The model takes into account the impacts of noise, time delay and public sensitivity on infectious illness propagation. The stochastic dynamics of the system are analyzed at the Hopf bifurcation, using time delay and noise intensity as bifurcation parameters, and the theoretical conclusions are validated using numerical simulation. Increasing the time delay and sensitivity coefficient can effectively delay the occurrence of the peak number of infected individuals and mitigate the extent of infection. Additionally, time delay and noise intensity are shown to have specific thresholds, beyond which periodic infections occur. Notably, heightened public sensitivity reduces the threshold for time delay, and media publicity directly affects public sensitivity. The numerical simulation reveals that increasing media publicity intensity does not always yield better results, and that the sensitivity of the public at present is an important reference index for setting an appropriate publicity intensity.
- noise,
- time delay,
- SEAQVR model,
- sensitivity coefficient,
- Hopf bifurcation
Citation: Chang Hou, Qiubao Wang. The influence of an appropriate reporting time and publicity intensity on the spread of infectious diseases[J]. AIMS Mathematics, 2023, 8(10): 23578-23602. doi: 10.3934/math.20231199

Related Papers:

Abstract

We present a stochastic time-delay susceptible-exposed-asymptomatic-symptom-vaccinated-recovered (SEAQVR) model with media publicity effect in this study. The model takes into account the impacts of noise, time delay and public sensitivity on infectious illness propagation. The stochastic dynamics of the system are analyzed at the Hopf bifurcation, using time delay and noise intensity as bifurcation parameters, and the theoretical conclusions are validated using numerical simulation. Increasing the time delay and sensitivity coefficient can effectively delay the occurrence of the peak number of infected individuals and mitigate the extent of infection. Additionally, time delay and noise intensity are shown to have specific thresholds, beyond which periodic infections occur. Notably, heightened public sensitivity reduces the threshold for time delay, and media publicity directly affects public sensitivity. The numerical simulation reveals that increasing media publicity intensity does not always yield better results, and that the sensitivity of the public at present is an important reference index for setting an appropriate publicity intensity.

References

[1]	J. Bedford, J. Farrar, C. Ihekweazu, G. Kang, M. Koopmans, J. Nkengasong, A new twenty-first century science for effective epidemic response, Nature, 575 (2019), 130–136. https://doi.org/10.1038/s41586-019-1717-y doi: 10.1038/s41586-019-1717-y
[2]	D. E. Bloom, D. Cadarette, Infectious disease threats in the 21st century: strengthening the global response, Front. Immunol., 10 (2019). https://doi.org/10.3389/fimmu.2019.00549 doi: 10.3389/fimmu.2019.00549
[3]	W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Royal Soc. London. Series A, 115 (1927), 700–721. https://doi.org/10.1098/rspa.1927.0118 doi: 10.1098/rspa.1927.0118
[4]	I. Korolev, Identification and estimation of the SEIRD epidemic model for COVID-19, J. Econometrics, 220 (2021), 63–85. https://doi.org/10.1016/j.jeconom.2020.07.038 doi: 10.1016/j.jeconom.2020.07.038
[5]	L. Basnarkov, SEAIR Epidemic spreading model of COVID-19, Chaos Solitons Fract., 142 (2021), 110394. https://doi.org/10.1016/j.chaos.2020.110394 doi: 10.1016/j.chaos.2020.110394
[6]	Z. Y. He, A. Abbes, H. Jahanshahi, N. D. Alotaibi, Y. Wang, Fractional-order discrete-time SIR epidemic model with vaccination: chaos and complexity, Mathematics, 10 (2022), 165. https://doi.org/10.3390/math10020165 doi: 10.3390/math10020165
[7]	X. Meng, Z. Cai, S. Si, D. Duan, Analysis of epidemic vaccination strategies on heterogeneous networks: based on SEIRV model and evolutionary game, Appl. Math. Comput., 403 (2021), 126172. https://doi.org/10.1016/j.amc.2021.126172 doi: 10.1016/j.amc.2021.126172
[8]	K. Goel, A mathematical and numerical study of a SIR epidemic model with time delay, nonlinear incidence and treatment rates, Theory Biosci., 138 (2019), 203–213. https://doi.org/10.1007/s12064-019-00275-5 doi: 10.1007/s12064-019-00275-5
[9]	Y. Liu, J. A. Cui, The impact of media coverage on the dynamics of infectious disease, Int. J. Biomath., 1 (2008), 65–74. https://doi.org/10.1142/S1793524508000023 doi: 10.1142/S1793524508000023
[10]	I. Z. Kiss, J. Cassell, M. Recker, P. L. Simon, The impact of information transmission on epidemic outbreaks, Math Biosci., 225 (2010), 1–10. https://doi.org/10.1016/j.mbs.2009.11.009 doi: 10.1016/j.mbs.2009.11.009
[11]	Y. Xiao, S. Tang, J. Wu, Media impact switching surface during an infectious disease outbreak, Sci. Rep., 5 (2015), 1–19. https://doi.org/10.1038/srep07838 doi: 10.1038/srep07838
[12]	D. Stellmach, I. Beshar, J. Bedford, P. Du Cros, Anthropology in public health emergencies: what is anthropology good for? BMJ Global Health, 3 (2018), e000534. http://dx.doi.org/10.1136/bmjgh-2017-000534 doi: 10.1136/bmjgh-2017-000534
[13]	S. J. Heine, Cultural Psychology, New York: John Wiley and Sons, 2010. https://doi.org/10.1002/9780470561119.socpsy002037
[14]	J. Wu, R. Zuo, C. He, H. Xiong, K. Zhao, Z. Hu, The effect of information literacy heterogeneity on epidemic spreading in information and epidemic coupled multiplex networks, Physica A: Statist. Mech. Appl., 596 (2022), 127119. https://doi.org/10.1016/j.physa.2022.127119 doi: 10.1016/j.physa.2022.127119
[15]	G. D.Webster, J. L. Howell, J. E. Losee, E. A. Mahar, V. Wongsomboon, Culture, COVID-19, and collectivism: A paradox of American exceptionalism? Pers. Indiv. Differ., 178 (2021), 110853. https://doi.org/10.1016/j.paid.2021.110853 doi: 10.1016/j.paid.2021.110853
[16]	A. K. Misra, A. Sharma, J. B. Shukla, Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases, Math. Comput. Model., 53 (2011), 1221–1228. https://doi.org/10.1016/j.mcm.2010.12.005 doi: 10.1016/j.mcm.2010.12.005
[17]	E. Gutierrez, A. Rubli, T. Tavares, Information and behavioral responses during a pandemic: evidence from delays in COVID-19 death reports, J. Dev. Econ., 154 (2022), 102774. https://doi.org/10.1016/j.jdeveco.2021.102774 doi: 10.1016/j.jdeveco.2021.102774
[18]	Y. Cai, Y. Kang, M. Banerjee, W. Wang, A stochastic SIRS epidemic model with infectious force under intervention strategies, J. Differ. Equ., 259 (2015), 7463–7502. https://doi.org/10.1016/j.jde.2015.08.024 doi: 10.1016/j.jde.2015.08.024
[19]	Q. Liu, D. Jiang, T. Hayat, A. Alsaedi, Dynamical behavior of a stochastic epidemic model for cholera, J. Franklin Inst., 356 (2019), 7486–7514. https://doi.org/10.1016/j.jfranklin.2018.11.056 doi: 10.1016/j.jfranklin.2018.11.056
[20]	B. Zhou, X. Zhang, D. Jiang, Dynamics and density function analysis of a stochastic SVI epidemic model with half saturated incidence rate, Chaos Solitons Fract., 137 (2020), 109865. https://doi.org/10.1016/j.chaos.2020.109865 doi: 10.1016/j.chaos.2020.109865
[21]	F. Li, S. Zhang, X. Meng, Dynamics analysis and numerical simulations of a delayed stochastic epidemic model subject to a general response function, Comput. Appl. Math., 38 (2019), 1–30. https://doi.org/10.1007/s40314-019-0857-x doi: 10.1007/s40314-019-0857-x
[22]	K. Iwata, C. Miyakoshi, A simulation on potential secondary spread of novel coronavirus in an exported country using a stochastic epidemic SEIR model, J. Clin. Med., 9 (2020), 944. https://doi.org/10.3390/jcm9040944 doi: 10.3390/jcm9040944
[23]	P. Grandits, R. M. Kovacevic, V. M. Veliov, Optimal control and the value of information for a stochastic epidemiological SIS-model, J. Math. Anal. Appl., 476 (2019), 665–695. https://doi.org/10.1016/j.jmaa.2019.04.005 doi: 10.1016/j.jmaa.2019.04.005
[24]	A. Din, Y. Li, A. Yusuf, Delayed hepatitis B epidemic model with stochastic analysis, Chaos Solitons Fract., 146 (2021), 110839. https://doi.org/10.1016/j.chaos.2021.110839 doi: 10.1016/j.chaos.2021.110839
[25]	A. L. Krause, L. Kurowski, K. Yawar, R. A. Van Gorder, Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies, J. Theor. Biol., 449 (2018), 35–52. https://doi.org/10.1016/j.jtbi.2018.04.023 doi: 10.1016/j.jtbi.2018.04.023
[26]	L. J. Allen, E. J. Allen, A comparison of three different stochastic population models with regard to persistence time, Theor. Popul. Biol., 64 (2003), 439–449. https://doi.org/10.1016/S0040-5809(03)00104-7 doi: 10.1016/S0040-5809(03)00104-7
[27]	S. Okyere, J. A. Prah, A. N. O. Sarpong, An Optimal Control Model of the transmission dynamics of COVID-19 in Ghana, preprint paper, 2022. https://doi.org/10.48550/arXiv.2202.06413
[28]	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. https://doi.org/10.1016/S0025-5564(02)00108-6 doi: 10.1016/S0025-5564(02)00108-6
[29]	Z. Han, Q. Wang, H. Wu, Z. Hu, Stochastic P-bifurcation in a delayed Myc/E2F/miR-17-92 network, Int. J. Bifurcat. Chaos, 32 (2022), 2250159. https://doi.org/10.1142/S0218127422501590 doi: 10.1142/S0218127422501590
[30]	X. Zhang, J. Fu, S. Hua, H. Liang, Z. K. Zhang, Complexity of Government response to COVID-19 pandemic: a perspective of coupled dynamics on information heterogeneity and epidemic outbreak, Nonlinear Dynam., 2013 (2013), 1–20. https://doi.org/10.1007/s11071-023-08427-5 doi: 10.1007/s11071-023-08427-5
[31]	S. H. Oh, S. Y. Lee, C. Han, The effects of social media use on preventive behaviors during infectious disease outbreaks: the mediating role of self-relevant emotions and public risk perception, Health Commun., 36 (2021), 972–981. https://doi.org/10.1080/10410236.2020.1724639 doi: 10.1080/10410236.2020.1724639
[32]	H. Huang, Y. Chen, Y. Ma, Modeling the competitive diffusions of rumor and knowledge and the impacts on epidemic spreading, Appl. Math. Comput., 388 (2021), 125536. https://doi.org/10.1016/j.amc.2020.125536 doi: 10.1016/j.amc.2020.125536
[33]	D. H. Morris, F. W. Rossine, J. B. Plotkin, S. A. Levin, Optimal, near-optimal, and robust epidemic control, Commun. Phys., 4 (2021), 78. https://doi.org/10.1038/s42005-021-00570-y doi: 10.1038/s42005-021-00570-y

Reader Comments

Your name:*

Email:*
© 2023 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)