COVID-19, a contagious respiratory disease, presents immediate and unforeseen challenges to people worldwide. Moreover, its transmission rapidly extends globally due to its viral transmissibility, emergence of novel strains (variants), absence of immunity, and human unawareness. This framework introduces a revised epidemic model, drawing upon mathematical principles. This model incorporates a modified vaccination and lockdown approach to comprehensively depict an epidemic’s transmission, containment, and decision-making processes within a community. This study aims to provide policymakers with precise information on real-world situations to assist them in making informed decisions about the implementation of lockdown strategies, maintenance variables, and vaccine availability. The suggested model has conducted stability analysis, strength number analysis, and first and second-order derivative analysis of the Lyapunov function and has established the existence and uniqueness of solutions of the proposed models. We examine the combined effects of an effective vaccination campaign and non-pharmaceutical measures such as lockdowns and states of emergency. We rely on the results of this research to assist policymakers in various countries in eradicating the illness by developing more innovative measures to control the outbreak.
Li, R.Y.M., Yue, X.G. and Crabbe, M.J.C. (2021) COVID-19 in Wuhan, China: Pressing Realities and City Management. Frontiers in Public Health, 8, Article 596913. https://doi.org/10.3389/fpubh.2020.596913
[3]
Anderson, R.M. and May, R.M. (1979) Population Biology of Infectious Disease: Part I. Nature, 280, 361-367. https://doi.org/10.1038/280361a0
[4]
Ross, R. (1916) An Application of the Theory of Probabilities to the Study of a Priori Pathometry—Part I. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 92, 204-230. https://doi.org/10.1098/rspa.1916.0007
[5]
Kermack, W.O. and McKendrick, A.G. (1927) A Contribution to the Mathematical Theory of Epidemics, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 115, 700-721. https://doi.org/10.1098/rspa.1927.0118
[6]
Bailey Norman, T.J. (1975) The Mathematical Theory of Infectious Diseases and Its Applications. 2nd Edition, Griffin, London.
[7]
Anderson, R.M.(1982) Population Dynamics of Infectious Diseases: Theory and Applications. Chapman and Hall, London.
[8]
Brauer, F., Castillo-Chavez, C. and Castillo-Chavez, C. (2012) Mathematical Models in Population Biology and Epidemiology. Springer, New York. https://doi.org/10.1007/978-1-4614-1686-9
[9]
Martcheva, M. (2015) An Introduction to Mathematical Epidemiology. Springer, New York. https://doi.org/10.1007/978-1-4899-7612-3
[10]
Michael, Y.L. (2017) An Introduction to Mathematical Modeling of Infectious Diseases. Springer, New York.
[11]
Kabir, K.M.A. and Tanimoto, J. (2020) Evolutionary Game Theory Modeling to Represent the Behavioral Dynamics of Economic Shutdowns and Shield Immunity in the COVID-19 Pandemic. Royal Society Open Science, 7, Article ID: 201095. https://doi.org/10.1098/rsos.201095
[12]
Kabir, K.M.A., Risa, T. and Tanimoto, J. (2021) Prosocial Behavior of Wearing a Mask during an Epidemic: An Evolutionary Explanation. Scientific Reports, 11, Article No. 12621. https://doi.org/10.1038/s41598-021-92094-2
[13]
Alam, M., Kabir, K.M.A. and Tanimoto, J. (2020) Based on Mathematical Epidemiology and Evolutionary Game Theory, Which Is More Effective: Quarantine or Isolation Policy? Journal of Statistical Mechanics: Theory and Experiment, 2020, Article ID: 033502. https://doi.org/10.1088/1742-5468/ab75ea
[14]
Higazy, M., Allehiany, F.M. and Mahmoud, E.E. (2021) Numerical Study of Fractional-Order COVID-19 Pandemic Transmission Model in the Context of ABO Blood Group. Results in Physics, 22, Article ID: 103852. https://doi.org/10.1016/j.rinp.2021.103852
[15]
Ullah, M.S., Higazy, M. and Kabir, K.M.A. (2021) Modeling the Epidemic Control Measures in Overcoming COVID-19 Outbreaks: A Fractional-Order Derivative Approach. Chaos, Solitons & Fractals, 155, Article ID: 111636. https://doi.org/10.1016/j.chaos.2021.111636
[16]
Higazy, M. and Alyami, M.A. (2020) New Caputo-Fabrizio Fractional-Order SEIASqEqHR Model for COVID-19 Epidemic Transmission with Genetic Algorithm-Based Control Strategy. Alexandria Engineering Journal, 59, 4719-4736.
[17]
Das, P., Nadim, S.S., Das, S., et al. (2021) Dynamics of COVID-19 Transmission with Comorbidity: A Data Driven Modelling Based Approach. Nonlinear Dynamics, 106, 1197-1211. https://doi.org/10.1007/s11071-021-06324-3
[18]
Islam, M.S., Ira, J.I., Kabir, K.M.A. and Kamrujjaman, M. (2020) Effect of Lockdown and Isolation to Suppress the COVID-19 in Bangladesh: An Epidemic Compartments Model. Journal of Mathematical Analysis and Applications, 4, 83-93. https://doi.org/10.26855/jamc.2020.09.004
[19]
Chowdhury, A., Kabir, K.M.A. and Tanimoto, J. (2020) How to Quarantine and Social-Distancing Policy Can Suppress the Outbreak of Novel Coronavirus in Developing or under Poverty Level Countries: A Mathematical and Statistical Analysis. https://doi.org/10.21203/rs.3.rs-20294/v1
[20]
Das, P., Upadhyay, R.K., Misra, A.K., et al. (2021) Mathematical Model of COVID-19 with Comorbidity and Controlling Using Non-Pharmaceutical Interventions and Vaccination. Nonlinear Dynamics, 106, 1213-1227. https://doi.org/10.1007/s11071-021-06517-w
[21]
Anderson, R.M. and May, R.M. (1985) Vaccination and Herd Immunity to Infectious Diseases. Nature, 318, 323-329. https://doi.org/10.1038/318323a0
[22]
Struchiner, C.J., Halloran, M.E. and Spielman, A. (1989) Modeling Malaria Vaccines I: New Uses for Old Ideas. Mathematical Biosciences, 94, 837-113. https://doi.org/10.1016/0025-5564(89)90073-4
[23]
Galvani, A.P., Reluga, T.C. and Chapman, G.B. (2007) Long-Standing Influenza Vaccination Policy Is in Accord with Individual Self-Interest But Not with the Utilitarian Optimum. Proceedings of the National Academy of Sciences of the United States of America, 104, 5692-5697. https://doi.org/10.1073/pnas.0606774104
[24]
Anderson, R.M. and May, R.M. (1992) Infectious Diseases of Humans. Oxford Academic, Oxford. https://doi.org/10.1093/oso/9780198545996.001.0001
[25]
Coburn, B.J., Wagner, B.G. and Blower, S. (2009) Modeling Influenza Epidemics and Pandemics: Insights into the Future of Swine Flu (H1N1). BMC Medicine, 7, Article No. 30. https://doi.org/10.1186/1741-7015-7-30
[26]
Longini, I.M., Halloran, J.M.E., Nizam, A. and Yang, Y. (2004) Containing Pandemic Influenza with Antiviral Agents. American Journal of Epidemiology, 159, 623-633. https://doi.org/10.1093/aje/kwh092
[27]
Viboud, C., Boelle, P.Y., Carrat, F., Valleron, A.J. and Flahault, A. (2000) Prediction of the Spread of Influenza Epidemics by the Method of Analogues. American Journal of Epidemiology, 158, 996-1006. https://doi.org/10.1093/aje/kwg239
[28]
Viboud, C., Boelle, P.Y., Pakdaman, K., Carrat, F., Valleron, A.J. and Flahault, A. (2004) Influenza Epidemics in the United States, France, and Australia, 1972-1997. Emerging Infectious Diseases, 10, 32-39. https://doi.org/10.3201/eid1001.020705
[29]
Choi, Y., Kim, J.S., Kim, J.E., Choi, H. and Lee, C.H. (2021) Vaccination Prioritization Strategies for COVID-19 in Korea: A Mathematical Modeling Approach. International Journal of Environmental Research and Public Health, 18, Article 4240. https://doi.org/10.3390/ijerph18084240
[30]
MacIntyre, C.R., Costantino, V. and Trent, M. (2020) Modelling of COVID-19 Vaccination Strategies and Herd Immunity, in Scenarios of Limited and Full Vaccine Supply in NSW, Australia (Under Review). https://doi.org/10.1101/2020.12.15.20248278
[31]
Chen, F. (2018) Voluntary Vaccinations and Vaccine Shortages: A Theoretical Analysis. Journal of Theoretical Biology, 446, 19-32. https://doi.org/10.1016/j.jtbi.2018.02.032
[32]
Li, Z., Xu, J., Xu, J., Tan, T. and Zhang, C. (2020) Current Situation, Causes, and Countermeasures to NIP Vaccine Shortages in Guangzhou, China. Human Vaccines &Immunotherapeutics, 16, 76-79. https://doi.org/10.1080/21645515.2019.1644883
[33]
Kahwati, L.C., Elter, J.R., Straits-Tröster, K.A. Kinsinger, L.S. and Davey, V.J. (2007) The Impact of the 2004-2005 Influenza Vaccine Shortage in the Veterans Health Administration. Journal of General Internal Medicine, 22, 1132-1138. https://doi.org/10.1007/s11606-007-0249-6
[34]
Fairbrother, G., Broder, K., Staat, M.A., Schwartz, B., Heubi, C., Hiratzka, S., Walker, F.J. and Morrow, A.L. (2007) Pediatricians’ Adherence to Pneumococcal Conjugate Vaccine Shortage Recommendations in 2 National Shortages. Pediatrics, 120, e401-e409. https://doi.org/10.1542/peds.2007-0359
[35]
Allison, T.C., Wells, M.S.K., Seib, K., Kudis, A., Hannan, C., Orenstein, W.A., Whitney, E.A.S., Hinman, A.R., Buehler, J.W., Omer, S.B. and Berkelman, R.L. (2012) Lessons Learned from the 2007 to 2009 Haemophilus influenzae Type B Vaccine Shortage. Journal of Public Health Management and Practice, 18, E9-E16. https://doi.org/10.1097/PHH.0b013e31821dce27
[36]
Walter, W. (1998) Ordinary Differential Equations. Springer, New York. https://doi.org/10.1007/978-1-4612-0601-9
[37]
Nabi, K.N., Abboubakar, H. and Kumar, P. (2020) Forecasting of Covid-19 Pandemic: From Integer Derivatives to Fractional Derivatives. Chaos, Solitons & Fractals, 141, Article ID: 110283. https://doi.org/10.1016/j.chaos.2020.110283
[38]
Kamrujjaman, M., Mahmud, M.S., Ahmed, S., Qayum, M.O., Alam, M.M., Hassan, M.N., Islam, M.R., Nipa, K.F. and Bulut, U. (2021) SARS-CoV-2 and Rohingya Refugee Camp, Bangladesh: Uncertainty and How the Government Took over the Situation. Biology, 10, Article 124. https://doi.org/10.3390/biology
[39]
Mahmud, M.S., Kamrujjaman, M., Adan, M.M.I.Y., et al. (2022) Vaccine Efficacy and SARS-CoV-2 Control in California and US during the Session 2020-e2026: A Modeling Study. Infectious Disease Modelling, 7, 62-81. https://doi.org/10.1016/j.idm.2021.11.002
[40]
Kamrujjaman, M., Saha, P., Islam, M.S., et al. (2022) Dynamics of SEIR Model: A Case Study of COVID-19 in Italy. Results in Control and Optimization, 7, Article ID: 100119. https://doi.org/10.1016/j.rico.2022.100119
[41]
Islam, M.R., Gray, M.J. and Peace, A. (2021) Identifying the Dominant Transmission Pathway in a Multi-Stage Infection Model of the Emerging Fungal Pathogen Batrachochytrium salamandrivorans on the Eastern Newt. In: Teboh-Ewungkem, M.I. and Ngwa, G.A., Eds., Infectious Diseases and Our Planet, Springer, Cham, 193-216. https://doi.org/10.1007/978-3-030-50826-5_7
[42]
Yorke, J.A. (1967) Invariance for Ordinary Differential Equations. Mathematical Systems Theory, 1, 353-372. https://doi.org/10.1007/BF01695169
[43]
Diekmann, O. and Heesterbeek, J.A.P. (2000) Mathematical Models in Population Biology and Epidemiology. Springer, New York.
[44]
Atangana, A. (2021) Mathematical Model of Survival of Fractional Calculus, Critics and Their Impact: How Singular Is Our World? Advances in Difference Equations, 2021, Article No. 403. https://doi.org/10.1186/s13662-021-03494-7
[45]
Wikipedia: COVID-19 Pandemic in Bangladesh.
[46]
AAAS (2020) Just 50% of Americans Plan to Get a COVID-19 Vaccine. Here’s How to Win over the Rest.
[47]
Pew Research Center (2020) US Public Now Divided over Whether to Get COVID-19 Vaccine.
[48]
BBC News (2021) COVID: India Sees the World’s Highest Daily Cases Amid Oxygen Shortage.
