Mathematical modelling has been widely used in many fields, especially in recent years. The applications of mathematical modelling in infectious diseases have shown that situations such as isolation, quarantine, vaccination and treatment are often necessary to eliminate most infectious diseases. In this study, a mathematical model of COVID-19 disease involving susceptible (S), exposed (E), infected (I), quarantined (Q), vaccinated (V) and recovered (R) populations is considered. In order to show the biological significance of the system, the non-negative solution region and the boundedness of the relevant biological compartments are shown. The endemic and disease-free equilibrium points of the model are calculated, and local stability analyses of these equilibrium points are performed. The basic reproduction number is also calculated for the relevant model. Sensitivity analysis of this number is studied, and it has been pointed out which parameters affect this number and how they affect it. Moreover, using real data from Iraq, the model parameters are estimated using the least squares curve fitting method, and numerical simulations are performed by using these estimated values. For the solution of the model, the Adams-Bashforth type predictive-corrective numerical method is used, and with the help of numerical simulations, several predictions are achieved about the future course of COVID-19.
Citation: Mehmet Yavuz, Waled Yavız Ahmed Haydar. A new mathematical modelling and parameter estimation of COVID-19: a case study in Iraq[J]. AIMS Bioengineering, 2022, 9(4): 420-446. doi: 10.3934/bioeng.2022030
Mathematical modelling has been widely used in many fields, especially in recent years. The applications of mathematical modelling in infectious diseases have shown that situations such as isolation, quarantine, vaccination and treatment are often necessary to eliminate most infectious diseases. In this study, a mathematical model of COVID-19 disease involving susceptible (S), exposed (E), infected (I), quarantined (Q), vaccinated (V) and recovered (R) populations is considered. In order to show the biological significance of the system, the non-negative solution region and the boundedness of the relevant biological compartments are shown. The endemic and disease-free equilibrium points of the model are calculated, and local stability analyses of these equilibrium points are performed. The basic reproduction number is also calculated for the relevant model. Sensitivity analysis of this number is studied, and it has been pointed out which parameters affect this number and how they affect it. Moreover, using real data from Iraq, the model parameters are estimated using the least squares curve fitting method, and numerical simulations are performed by using these estimated values. For the solution of the model, the Adams-Bashforth type predictive-corrective numerical method is used, and with the help of numerical simulations, several predictions are achieved about the future course of COVID-19.
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Mehmet Yavuz, Waled Yavız Ahmed Haydar. A new mathematical modelling and parameter estimation of COVID-19: a case study in Iraq[J]. AIMS Bioengineering, 2022, 9(4): 420-446. doi: 10.3934/bioeng.2022030
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