Mathematical modeling of COVID-19 spread with media coverage and optimal control analysis

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 08 خرداد 1404   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.92605.1612

نویسندگان

G.P. Sahu؛ A.S. Thakur^*

Center for Basic Sciences, Pt. Ravishankar Shukla University, Raipur, Chhattisgarh, India.

چکیده

The COVID-19 pandemic, initiated by the SARS-CoV-2 virus, first emerged in Wuhan, China and quickly propagated worldwide. In India, lacking immediate access to effective vaccines and antiviral drugs, the response primarily relied on nonpharmaceutical interventions. These strategies, extensively covered by the media, were vital in promoting preventive behaviors to limit viral transmission. This research introduces a new mathematical model, SAEIaIRU M , to analyze COVID-19’s transmission dynamics. It includes a saturation functional response to depict the media’s role in influencing public behavior. The control reproduction number (Rc) is determined, and both local and global stability of the disease-free equilibrium are analyzed. Using the least-squares method, the model fits daily case data from India from March 30, 2020, to January 24, 2021. We evaluate the impact of various control parameters on disease progression through numerical simulations and employ normalized forward sensitivity analysis to identify critical parameters affecting Rc. The study advances by for mulating an optimal control problem, incorporating the cost of preventive actions as control variables. Findings indicate that an early optimal control strategy could lessen the severity of epidemic peaks by distributing their effects over a longer duration. Simulations demonstrate that combining four control measures outperforms a single or no control. 

کلیدواژه‌ها

COVID-19؛ Environmental transmission؛ Saturated awareness؛ Optimal control

مراجع

[1] Alanazi, K.M. The asymptotic spreading speeds of COVID-19 with the effect of delay and quarantine, AIMS Math. 9(7) (2024), 19397–19413.
[2] Aldila, D. Analyzing the impact of the media campaign and rapid testing for COVID-19 as an optimal control problem in East Java, Indonesia, Chaos, Solitons Fractals, 141 (2020), 110364.

[3] Aldila, D., Khoshnaw, S.H.A., Safitri, E., Anwar, Y.R., Bakry, A.R.Q., Samiadji, B.M., Anugerah, D.A., Gh, M.F. A., Ayulani, I.D. and Salim, S.N. A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia, Chaos Solitons Fractals, 139 (2020), 110042.
[4] Anderson, R.M., Heesterbeek, H., Klinkenberg, D. and Hollingsworth, D.T. How will country-based mitigation measures influence the course of the COVID-19 epidemic ?, The Lancet, 395 (10228) (2020), 931–934.
[5] Asamoah, J.K.K., Owusu, M.A., Jin, Z., Oduro, F.T., Abidemi, A. and Gyasi, E.O. Global stability and cost-effectiveness analysis of COVID- 19 considering the impact of the environment: using data from Ghana, Chaos, Solitons Fractals, 140 (2020), 110103.
[6] Atangana, A. and İğret, A.S. Mathematical model of COVID-19 spread in Turkey and South Africa: theory, methods, and applications, Adv. Differ. Equ. 2020(1) (2020), 1–89.
[7] Bajiya, V.P., Bugalia, S., Tripathi, J.P. and Martcheva, M. Deciphering the transmission dynamics of COVID- 19 in India: optimal control and cost effective analysis, J. Biol. Dyn. 16(1) (2022), 665–712.
[8] Baroudi, M., Laarabi, H., Zouhri, S., Rachik, M. and Abta, A. Stochastic optimal control model for COVID-19: mask wearing and active screening/testing, J. Appl. Math. Comput. 70(6) (2024), 6411–6441.
[9] BBC, News https://www.bbc.com/news/ world-asia-india-52077395 (Accessed: June, 2022).
[10] Birkhoff, G. and Rota, G. Ordinary Differential Equations, Wiley, United Kingdom, 1978.
[11] Castillo-Chavez, C. and Song, B. Dynamical models of tuberculosis and their applications, Math. Biosci. Eng. 1(2) (2004), 361–404.
[12] Chang, X., Liu, M., Jin, Z. and Wang, J. Studying on the impact of media coverage on the spread of COVID-19 in Hubei Province, China, Math. Biosci. Eng. 17(4) (2020), 3147–3159.

[13] Chen, K., Pun, C.S. and Wong, H.Y. Efficient social distancing during the COVID-19 pandemic: integrating economic and public health considerations, European J. Oper. Res. 304(1) (2023), 84–98.
[14] Chen, N., Zhou, M., Dong, X., Qu, J., Gong, F., Han, Y., Qiu, Y., Wang, J., Liu, Y., Wei, Y. and Xia, J.A. Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: a descriptive study, The Lancet, 395(10223) (2020), 507–513.
[15] Chen, T., Li, Z. and Zhang, G. Analysis of a COVID-19 model with media coverage and limited resources, Math. Biosci. Eng. 21(4) (2024), 5283–5307.
[16] Cheneke, K. Optimal control analysis for modeling HIV transmission, Iran. J. Numer. Anal. Optim. 13(4) (2023), 747–762.
[17] Cucinotta, D. and Vanelli, M. WHO declares COVID-19 a pandemic, Acta Biomed. 91(1) (2020), 157.
[18] d’Onofrio, A., Iannelli, M., Manfredi, P. and Marinoschi, G. Epidemic control by social distancing and vaccination: optimal strategies and remarks on the COVID-19 Italian response policy, Math. Biosci. Eng. 21(7) (2024), 6493–6520.
[19] Dwivedi, S., Perumal, S.K., Kumar, S., Bhattacharyya, S. and Kumari, N. Impact of cross border reverse migration in Delhi- UP region of India during COVID-19 lockdown, Comput. Math. Biophys. 11 (2023), 1–26.
[20] Gholami, M., Mirhosseini, A.S. and Heidari, A. Designing a sliding mode controller for a class of multi-controller COVID-19 disease model, Iran. J. Numer. Anal. Optim. 15(1) (2025), 27–53.
[21] Ghosh, I., Tiwari, P.K., Samanta, S., Elmojtaba, I.M., Al-Salti, N. and Chattopadhyay, J. A simple SI-type model for HIV/AIDS with media and self-imposed psychological fear, Math. Biosci. 306 (2018), 160–169.
[22] Government of India https://www.mygov.in/covid-19 (Accessed: June, 2022).

[23] Guo, Y. and Li, T. Modeling the competitive transmission of the Omicron strain and Delta strain of COVID-19, J. Math. Anal. Appl. 526(2) (2023), 127283.
[24] Gupta, S., Rajoria, Y.K. and Sahu, G.P. Mathematical Modelling on Dynamics of Multi-variant SARS-CoV-2 Virus: Estimating Delta and Omicron Variant Impact on COVID-19, IJAM 55(1) (2025), 180–188.
[25] Hao, J., Huang, L., Liu, M. and Ma, Y. Analysis of the COVID-19 model with self-protection and isolation measures affected by the environment, Math. Biosci. Eng. 21(4) (2024), 4835–4852.
[26] Huang, C., Wang, Y., Li, X., Ren, L., Zhao, J., Hu, Y., Zhang, L., Fan, G., Xu, J., Gu, X. and Cheng, Z. Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China, The lancet, 395(10223) (2020), 497–506.
[27] Humanitarian Data Exchange. Novel Coronavirus 2019 (COVID-19) Cases https://data.humdata.org/dataset/
novel-coronavirus-2019-ncov-cases#data-resources-0 (Accessed: June, 2023).
[28] Iboi, E., Sharomi, O.O., Ngonghala, C. and Gumel, A.B. Mathematical modeling and analysis of COVID-19 pandemic in Nigeria, MedRxiv, (2020), 1–24.
[29] Kahn, J.S. and McIntosh, K. History and recent advances in coronavirus discovery Pediatr. Infect. Dis. J. 24(11) (2005), S223–S227. 
[30] Killerby, M.E., Biggs, H.M., Midgley, C.M., Gerber, S.I. and Watson, J.T. Middle East respiratory syndrome coronavirus transmission Emerg. Infect. Dis. 26(2) (2020), 191.
[31] Koura, A.F., Raslan, K.R., Ali, K.K. and Shaalan, M.A. A numerical investigation for the COVID-19 spatiotemporal lockdown-vaccination model, Comput. Methods Differ. Equ. 12(4) (2024), 669–686.
[32] Kumar, A., Srivastava, P.K., Dong, Y., and Takeuchi, Y. Optimal control of infectious disease: Informationinduced vaccination and limited treatment, Phys. A: Stat. Mech. Appl. 542 (2020), 123196.

[33] Kurkina, E. and Koltsova, E. Mathematical modeling of the propagation of Covid-19 pandemic waves in the World, Comput. Math. Model. 32(2021), 147–170.
[34] Lakhal, M., Taki, R., El F.M. and El, G.T. Quarantine alone or in combination with treatment measures to control COVID-19, J. Anal. 31(4) (2023), 2347–2369.
[35] LaSalle, J.P. Stability theory and invariance principles, Elsevier, New York, 1976.
[36] Li, Q., Guan, X., Wu, P., Wang, X., Zhou, L., Tong, Y., Ren, R., Leung, K.S., Lau, E.H., Wong, J.Y. and Xing, X. Early transmission dynamics in Wuhan, China, of novel coronavirus infected pneumonia, N. Engl. J. Med. 382(13) (2020), 1199–1207.
[37] Liu, J. and Wang, X.S. Dynamic optimal allocation of medical resources: a case study of face masks during the first COVID-19 epidemic wave in the United States, Math. Biosci. Eng. 20(7) (2023), 12472–12485.
[38] Martcheva, M. An introduction to mathematical epidemiology, Springer, United States, 2015.
[39] Memon, Z., Qureshi, S. and Memon, B.R. Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: a case study, Chaos Solitons Fractals, 144 (2021), 110655.
[40] Misra, A., Sharma, A. and Shukla, J. Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases, Math. Comput. Model. 53(5-6) (2011), 1221–1228.
[41] Misra, A.K., Rai, R.K. and Takeuchi, Y. Modeling the control of infectious diseases: Effects of TV and social media advertisements, Math. Biosci. Eng. 15(6) (2018), 1315–1343.
[42] Rai, R.K., Khajanchi, S., Tiwari, P.K., Venturino, E. and Misra, A.K. Impact of social media advertisements on the transmission dynamics of COVID-19 pandemic in India, J. Appl. Math. Comput. (2022), 1–26.

[43] Sahu, G.P. and Dhar, J. Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate, Appl. Math. Model. 36(3) (2012), 908–923.
[44] Sahu, G.P. and Dhar, J. Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with preexisting immunity, J. Math. Anal. Appl. 421(2) (2015), 1651–1672.
[45] Sardar, T., Nadim, S.k.S., Rana, S. and Chattopadhyay, J. Assessment of lockdown effect in some states and overall India: a predictive mathematical study on COVID-19 outbreak, Chaos Solitons Fractals, 139 (2020), 1-10.
[46] Sarkar, K., Mondal, J. and Khajanchi, S. How do the contaminated environment influence the transmission dynamics of COVID-19 pandemic?, Eur. Phys. J: Spec. Top. 231(18-20) (2022), 3697–3716.
[47] Senapati, A., Rana, S., Das, T. and Chattopadhyay, J. Impact of intervention on the spread of COVID-19 in India: A model based study, J. Theor. Biol. 523 (2021) 110711.
[48] Sooknanan, J. and Comissiong, D. Trending on social media: integrating social media into infectious disease dynamics, Bull. Math. Biol. 82(7) (2020), 86.
[49] Sooknanan, J. and Mays, N. Harnessing social media in the modelling of pandemics challenges and opportunities, Bull. Math. Biol. 83(5) (2021), 57.
[50] Srivastav, A.K., Tiwari, P.K., Srivastava, P.K., Ghosh, M. and Kang, Y. A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic, Math. Biosci. Eng. 18(1) (2021), 182–213.
[51] Su, S., Wong, G., Shi, W., Liu, J., Lai, A.C.K., Zhou, J., Liu, W., Bi, Y. and Gao, G.F. Epidemiology, genetic recombination, and pathogenesis of coronaviruses, Trends Microbiol. 24(6) (2016), 490–502.

[52] Sun, D., Li, Y., Teng, Z., Zhang, T., and Lu, J. Dynamical properties in an SVEIR epidemic model with age-dependent vaccination, latency, infection, and relapse, Math. Methods Appl. Sci. 44(17) (2021), 12810–12834.
[53] Thakur, A.S. and Sahu, G.P. Modeling the COVID-19 Dynamics with Omicron Variant, Non-pharmaceutical Interventions, and Environmental Contamination Differ. Equations Dyn. Syst. (2025), 1–25.
[54] The Indian Express https://indianexpress.com/article/ coronavirus/coronavirus-india-infection-rate-china-6321154/
(Accessed: June, 2023).
[55] Van den Driessche, P. and Watmough, J. Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180(1-2) (2002), 29–48.
[56] Van Doremalen, N., Bushmaker, T., Morris, D.H., Holbrook, M.G., Gamble, A., Williamson, B.N., Tamin, A., Harcourt, J.L., Thornburg, N.J., Gerber, S.I. and Lloyd-Smith, J.O. Aerosol and surface stability of SARS-CoV- 2 as compared with SARS-CoV-1, N. Engl. J. Med. 382(16) (2020), 1564–1567.
[57] Wang, W. and Ruan, S. Bifurcation in an epidemic model with constant removal rate of the infectives, J. Math. Anal. Appl. 291(2) (2004), 775–793.
[58] Wang, X., Liang, Y., Li, J. and Liu, M. Modeling COVID-19 transmission dynamics incorporating media coverage and vaccination, Math. Biosci. Eng. 20 (2023), 10392–10403.
[59] Wardeh, M., Baylis, M. and Blagrove, M. S. Predicting mammalian hosts in which novel coronaviruses can be generated, Nat. Commun. 12(1) (2021), 780.
[60] Willman, M., Kobasa, D. and Kindrachuk, J.A. Comparative analysis of factors influencing two outbreaks of Middle Eastern respiratory syndrome (MERS) in Saudi Arabia and South Korea, Viruses 11(12) (2019), 1119.

[61] Yuan, R., Ma, Y., Shen, C., Zhao, J., Luo, X. and Liu, M. Global dynamics of COVID-19 epidemic model with recessive infection and isolation, Math. Biosci. Eng. 18(2) (2021), 1833–1844.
[62] Yuan, Y. and Li, N. Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness, Phys. A: Stat. Mech. Appl. 603 (2022), 127804.
[63] Zhao, S., Lin, Q., Ran, J., Musa, S.S., Yang, G., Wang, W., Lou, Y., Gao, D., Yang, L., He, D. and Wang, M.H. Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data driven analysis in the early phase of the outbreak, Int. J. Inf. Dis. 92 (2020), 214–217.