The spreading of COVID-19 has been considered a worldwide issue, and many global efforts have been suggested. Suggested control strategies to minimize the impact of the disease have effectively worked with computational simulations and mathematical models. Model critical transmissions and sensitivities are also key elements to study this pandemic more widely. This work reviews and discusses susceptible–exposed–infected–recovered (SEIR) model to predict the spreading of this disease. Accordingly, the basic reproduction number and its parameter elasticity are considered at the equilibrium points. Furthermore, the real data of confirmed cases in the Kurdistan region of Iraq are used in estimating model parameters and model validating. Computational model results provide some important model improvements and suggest control strategies. Firstly, the model population states have different model dynamics using the estimated parameters and the initial values. Another result is that almost all model states are sensitive to the model parameters at different levels. Interestingly, contact rate, transition rate from exposed class to the infected class and natural recovery rate are the most important controllable parameters to reduce the basic reproduction number R0, and they become the model critical parameters. More interestingly, computational results for the real data provide that the basic reproduction number in the Kurdistan Region was about 1.28, which is greater than unity. This means that the new coronavirus still has a high potential to spread among individuals, and it will require more interventions and new strategies to control this disease further.
Citation: Sarbaz H. A. Khoshnaw, Kawther Y. Abdulrahman, Arkan N. Mustafa. Identifying key critical model parameters in spreading of COVID-19 pandemic[J]. AIMS Bioengineering, 2022, 9(2): 163-177. doi: 10.3934/bioeng.2022012
The spreading of COVID-19 has been considered a worldwide issue, and many global efforts have been suggested. Suggested control strategies to minimize the impact of the disease have effectively worked with computational simulations and mathematical models. Model critical transmissions and sensitivities are also key elements to study this pandemic more widely. This work reviews and discusses susceptible–exposed–infected–recovered (SEIR) model to predict the spreading of this disease. Accordingly, the basic reproduction number and its parameter elasticity are considered at the equilibrium points. Furthermore, the real data of confirmed cases in the Kurdistan region of Iraq are used in estimating model parameters and model validating. Computational model results provide some important model improvements and suggest control strategies. Firstly, the model population states have different model dynamics using the estimated parameters and the initial values. Another result is that almost all model states are sensitive to the model parameters at different levels. Interestingly, contact rate, transition rate from exposed class to the infected class and natural recovery rate are the most important controllable parameters to reduce the basic reproduction number R0, and they become the model critical parameters. More interestingly, computational results for the real data provide that the basic reproduction number in the Kurdistan Region was about 1.28, which is greater than unity. This means that the new coronavirus still has a high potential to spread among individuals, and it will require more interventions and new strategies to control this disease further.
[1] | Li Q, Guan X, Wu P, et al. (2020) Early transmission dynamics in Wuhan, China, of novel coronavirus–infected pneumonia. N Engl J Med 382: 1199-1207. https://doi.org/10.1056/NEJMoa2001316 |
[2] | Gorbalenya AE, Baker SC, Baric R, et al. Severe acute respiratory syndrome-related coronavirus: The species and its viruses–a statement of the Coronavirus Study Group (2020). https://doi.org/10.1101/2020.02.07.937862 |
[3] | Chen N, Zhou M, Dong X, et al. (2020) Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: A descriptive study. The Lancet 395: 507-513. https://doi.org/10.1016/S0140-6736(20)30211-7 |
[4] | Huang C, Wang Y, Li X, et al. (2020) Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China. The Lancet 395: 497-506. https://doi.org/10.1016/S0140-6736(20)30183-5 |
[5] | Wang C, Horby PW, Hayden FG, et al. (2020) A novel coronavirus outbreak of global health concern. The Lancet 395: 470-473. https://doi.org/10.1016/S0140-6736(20)30185-9 |
[6] | Holshue ML, DeBolt C, Lindquist S, et al. (2020) First case of 2019 novel coronavirus in the United States. N Engl J Med 382: 929-936. https://doi.org/10.1056/NEJMoa2001191 |
[7] | WHO G, Statement on the second meeting of the International Health Regulations.Emergency Committee regarding the outbreak of novel coronavirus (2019-nCoV). World Health Organization, 2020 (2005) . Available from: https://www.who.int/news/item/30-01-2020-statement-on-the-second-meeting-of-the-international-health-regulations-(2005)-emergency-committee-regarding-the-outbreak-of-novel-coronavirus-(2019-ncov) |
[8] | Organization, W.H.WHO Director-General's opening remarks at the media briefing on COVID-19, 2020. Available from: https://reliefweb.int/report/world/who-director-generals-opening-remarks-media-briefing-covid-19-20-november-2020?gclid=CjwKCAjwur-SBhB6EiwA5sKtjlyi9UUQaeFUMljHfMiVkWeSgVVARurASa9mFnEB5GmjY95h2o2dKhoCHw8QAvD_BwE |
[9] | Coronavirus Outbreak [Internet] COVID-19 CORONAVIRUS PANDEMIC, 2020. Available from: https://www.worldometers.info/coronavirus/ |
[10] | World Health Organization, Coronavirus disease (COVID-19) situation report 153, 2020. Available from: https://apps.who.int/iris/handle/10665/332556 |
[11] | COVID J, dashboard by the center for systems science and engineering (CSSE) at Johns Hopkins university (JHU), 2020. Available from: https://coronavirus.jhu.edu/map.html |
[12] | Aldila D, Samiadji BM, Simorangkir GM, et al. (2021) Impact of early detection and vaccination strategy in COVID-19 eradication program in Jakarta, Indonesia. BMC Res Notes 14: 1-7. https://doi.org/10.1186/s13104-021-05540-9 |
[13] | Mekonen KG, Habtemicheal TG, Balcha SF (2021) Modeling the effect of contaminated objects for the transmission dynamics of COVID-19 pandemic with self-protection behavior changes. Results Appl Math 9: 100134. https://doi.org/10.1016/j.rinam.2020.100134 |
[14] | Aldila D, Khoshnaw SH, Safitri E, et al. (2020) A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia. Chaos Soliton Fract 139: 110042. https://doi.org/10.1016/j.chaos.2020.110042 |
[15] | Perasso A (2018) An introduction to the basic reproduction number in mathematical epidemiology. ESAIM: ProcS 62: 123-138. https://doi.org/10.1051/proc/201862123 |
[16] | Khajanchi S, Bera S, Roy TK (2021) Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes. Math Comput Simulat 180: 354-378. https://doi.org/10.1016/j.matcom.2020.09.009 |
[17] | Khoshnaw SH, Salih RH, Sulaimany S (2020) Mathematical modelling for coronavirus disease (COVID-19) in predicting future behaviours and sensitivity analysis. Math Model Nat Pheno 15: 33. https://doi.org/10.1051/mmnp/2020020 |
[18] | Khoshnaw SH, Shahzad M, Ali M, et al. (2020) A quantitative and qualitative analysis of the COVID–19 pandemic model. Chaos Soliton Fract 138: 109932. https://doi.org/10.1016/j.chaos.2020.109932 |
[19] | Khajanchi S, Nieto JJ (2021) Spatiotemporal dynamics of a glioma immune interaction model. Sci Rep 11: 22385. https://doi.org/10.1038/s41598-021-00985-1 |
[20] | Aldila D, Ndii MZ, Samiadji BM (2020) Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness. Math Biosci Eng 17: 6355-6389. https://doi.org/10.3934/mbe.2020335 |
[21] | Kouidere A, Kada D, Balatif O, et al. (2021) Optimal control approach of a mathematical modeling with multiple delays of the negative impact of delays in applying preventive precautions against the spread of the COVID-19 pandemic with a case study of Brazil and cost-effectiveness. Chaos Soliton Fract 142: 110438. https://doi.org/10.1016/j.chaos.2020.110438 |
[22] | Kouidere A, Youssoufi LE, Ferjouchia H, et al. (2021) Optimal control of mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with cost-effectiveness. Chaos Soliton Fract 145: 110777. https://doi.org/10.1016/j.chaos.2021.110777 |
[23] | Khajanchi S, Sarkar K, Banerjee S (2022) Modeling the dynamics of COVID-19 pandemic with implementation of intervention strategies. Eur Phys J Plus 137: 129. https://doi.org/10.1140/epjp/s13360-022-02347-w |
[24] | Mondal J, Khajanchi S Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak (2022). https://doi.org/10.1007/s11071-022-07235-7 |
[25] | Rai RK, Khajanchi S, Tiwari PK, et al. (2022) Impact of social media advertisements on the transmission dynamics of COVID-19 pandemic in India. J Appl Math Comput 68: 19-44. https://doi.org/10.1007/s12190-021-01507-y |
[26] | Khajanchi S, Sarkar K, Mondal J, et al. (2021) Mathematical modeling of the COVID-19 pandemic with intervention strategies. Results Phys 25: 104285. https://doi.org/10.1016/j.rinp.2021.104285 |
[27] | Khajanchi S, Sarkar K (2020) Forecasting the daily and cumulative number of cases for the COVID-19 pandemic in India. Chaos 30: 071101. https://doi.org/10.1063/5.0016240 |
[28] | Samui P, Mondal J, Khajanchi S (2020) A mathematical model for COVID-19 transmission dynamics with a case study of India. Chaos Soliton Fract 140: 110173. https://doi.org/10.1016/j.chaos.2020.110173 |
[29] | Sarkar K, Khajanchi S, Nieto JJ (2020) Modeling and forecasting the COVID-19 pandemic in India. Chaos Soliton Fract 139: 110049. https://doi.org/10.1016/j.chaos.2020.110049 |
[30] | Saito MM, Imoto S, Yamaguchi R, et al. (2013) Extension and verification of the SEIR model on the 2009 influenza A (H1N1) pandemic in Japan. Math Biosci 246: 47-54. https://doi.org/10.1016/j.mbs.2013.08.009 |
[31] | Diaz P, Constantine P, Kalmbach K, et al. (2018) A modified SEIR model for the spread of Ebola in Western Africa and metrics for resource allocation. Appl Math Comput 324: 141-155. https://doi.org/10.1016/j.amc.2017.11.039 |
[32] | Li MY, Graef JR, Wang L, et al. (1999) Global dynamics of a SEIR model with varying total population size. Math Biosci 160: 191-213. https://doi.org/10.1016/S0025-5564(99)00030-9 |
[33] | Chellaboina V, Bhat SP, Haddad WM, et al. (2009) Modeling and analysis of mass-action kinetics. IEEE Contr Syst Mag 29: 60-78. https://doi.org/10.1109/MCS.2009.932926 |
[34] | Khoshnaw SH Dynamic analysis of a predator and prey model with some computational simulations (2017) arXiv: 1709.00053. https://doi.org/10.4172/2329-9533.1000137 |
[35] | Diekmann O, Heesterbeek JAP, Metz JA (1990) On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J Math Biol 28: 365-382. https://link.springer.com/article/10.1007/BF00178324 |
[36] | Van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180: 29-48. https://doi.org/10.1016/S0025-5564(02)00108-6 |
[37] | Heffernan JM, Smith RJ, Wahl LM (2005) Perspectives on the basic reproductive ratio. J R Soc Interface 2: 281-293. https://doi.org/10.1098/rsif.2005.0042 |
[38] | Rahman B, Khoshnaw SH, Agaba GO, et al. (2021) How containment can effectively suppress the outbreak of COVID-19: a mathematical modeling. Axioms 10: 204. https://doi.org/10.3390/axioms10030204 |
[39] | Biegler LT, Damiano JJ, Blau GE (1986) Nonlinear parameter estimation: A case study comparison. AIChE J 32: 29-45. https://doi.org/10.1002/aic.690320105 |
[40] | Varah JM (1982) A spline least squares method for numerical parameter estimation in differential equations. SIAM J Sci Stat Comput 3: 28-46. https://doi.org/10.1137/0903003 |
[41] | Kurdistan Regional Government, GOV.KRD. Coronavirus(COVID-19). Available from: https://gov.krd/coronavirus-en/situation-update/ |