ABSTRACT
In this paper, we propose a COVID-19 epidemic model with quarantine class. The model contains 6 sub-populations, namely the susceptible (S), exposed (E), infected (I), quarantined (Q), recovered (R), and death (D) sub-populations. For the proposed model, we show the existence, uniqueness, non-negativity, and boundedness of solution. We obtain two equilibrium points, namely the disease-free equilibrium (DFE) point and the endemic equilibrium (EE) point. Applying the next generation matrix, we get the basic reproduction number (R0). It is found that R0 is inversely proportional to the quarantine rate as well as to the recovery rate of infected subpopulation. The DFE point always exists and if R0 < 1 then the DFE point is asymptotically stable, both locally and globally. On the other hand, if R0 > 1 then there exists an EE point, which is globally asymptotically stable. Here, there occurs a forward bifurcation driven by R0 . The dynamical properties of the proposed model have been verified our numerical simulations. © 2023 the author(s).
ABSTRACT
In this paper, we propose a COVID-19 epidemic model with quarantine class. The model contains 6 sub-populations, namely the susceptible (S), exposed (E), infected (I), quarantined (Q), recovered (R), and death (D) sub-populations. For the proposed model, we show the existence, uniqueness, non-negativity, and boundedness of solution. We obtain two equilibrium points, namely the disease-free equilibrium (DFE) point and the endemic equilibrium (EE) point. Applying the next generation matrix, we get the basic reproduction number (R0). It is found that R0 is inversely proportional to the quarantine rate as well as to the recovery rate of infected subpopulation. The DFE point always exists and if R0 < 1 then the DFE point is asymptotically stable, both locally and globally. On the other hand, if R0 > 1 then there exists an EE point, which is globally asymptotically stable. Here, there occurs a forward bifurcation driven by R0 . The dynamical properties of the proposed model have been verified our numerical simulations. © 2023 the author(s).
ABSTRACT
We discuss the dynamics of new COVID-19 epidemic model by considering asymptomatic infections and the policies such as quarantine, protection (adherence to health protocols), and vaccination. The proposed model contains nine subpopulations: Susceptible (S), exposed (E), symptomatic infected (I), asymptomatic infected (A), recovered (R), death (D), protected (P), quarantined (Q), and vaccinated (V). We first show the non-negativity and boundedness of solutions. The equilibrium points, basic reproduction number, and stability of equilibrium points, both locally and globally, are also investigated analytically. The proposed model has disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable if basic reproduction number is less than one. The endemic equilibrium point exists uniquely and is globally asymptotically stable if the basic reproduction number is greater than one. These properties have been confirmed by numerical simulations using the fourth order Runge-Kutta method. Numerical simulations show that the disease transmission rate of asymptomatic infection, quarantine rates, protection rate, and vaccination rates affect the basic reproduction number and hence also influence the stability of equilibrium points. © 2021 Published by Indonesian Biomathematical Society.
ABSTRACT
We consider a SEIQR epidemic model which describes the spread of COVID-19. The SEIQR epidemic model is built by introducing an isolation compartment in the SEIR model. We implement the variational iteration method (VIM) to find the approximate solution for the SEIQR model. We first implement the VIM by applying restricted variations for both linear and nonlinear terms in the correction functionals and find the Lagrange multiplier for the VIM. The comparison between the solution obtained by such VIM and the solution obtained by the fourth-order Runge-Kutta method shows that the VIM is accurate only for relatively small time domains. For larger time domains, the VIM solution is inaccurate and unrealistic. Then we improve the previous VIM by reducing the restricted variations and show that the improved VIM is more accurate than the previous VIM for larger time domains. © 2021 the author(s).
ABSTRACT
In this paper, five phenomenological (Richards, a generalized Richards, Blumberg, Tsoularis & Wallace, and Gompertz) models are implemented to predict the cumulative number of COVID-19 cases. The five phenomenological models are in the form of ordinary differential equations with a few number of model parameters. The model parameters of each model were calibrated by fitting the model with the reported cumulative number of COVID-19 cases in East Java Province from March 25 until October 31, 2020 via nonlinear least square method. We compare the performance of the five phenomenological models by measuring four performance metrics, namely the root mean square error (RMSE), the mean absolute error (MAE), the coefficient of determination (R-2) and the Akaike information criterion (AIC). When calibrating the cumulative number of cases, the five models perform very well, which are indicated by their high coefficient of determination (R-2 > 0.999). However, a comparison of the four-performance metrics shows that Tsoularis & Wallace performed the best followed by a generalized Richards model. The prediction for the final size of the COVID-19 epidemic in East Java according to the Tsoularis & Wallace model is kappa = 78 002. Both Richards and Gompertz models tend to underestimate the final size of the epidemic, while the Blumberg model tends to overestimate. The five models estimate the peak of the COVID-19 epidemic in East Java has been occurred on August 13-14, 2020. Using the predicted cumulative number of cases, we determine the daily new cases of COVID-19 in East Java. Based on the four-performance metrics, it appears that the five phenomenological models predict new daily cases of COVID-19 equally well.