Study of Dynamics of a COVID-19 Model for Saudi Arabia with Vaccination Rate, Saturated Treatment Function and Saturated Incidence Rate

This paper proposes, validates and analyzes the dynamics of the susceptible exposed infectious recovered (SEIR) model for the propagation of COVID-19 in Saudi Arabia, which recorded the largest number of cases in the Arab world. The model incorporates a saturated incidence rate, a constant vaccination rate and a nonlinear treatment function. The rate of treatment is assumed to be proportional to the number of infected persons when this number is low and reaches a fixed value for large number of infected individuals. The expression of the basic reproduction number is derived, and the model basic stability properties are studied. We show that when the basic reproduction number is less than one the model can predict both a Hopf and backward bifurcations. Simulations are also provided to fit the model to COVID-19 data in Saudi Arabia and to study the effects of the parameters of the treatment function and vaccination rate on disease control.

Modelling the evolution of the coronavirus disease (COVID-19) in Saudi Arabia.

INTRODUCTION: The ongoing COVID-19 pandemic has claimed hundreds of thousands of lives around the world. Health planners are seeking ways to forecast the evolution of the pandemic. In this study, a mathematical model was proposed for Saudi Arabia, the country with the highest reported number of COVID-19 cases in the Arab world. METHODOLOGY: The proposed model was adapted from the model used for the Middle East respiratory syndrome outbreak in South Korea. Using time-dependent parameters, the model incorporated the effects of both population-wide self-protective measures and government actions. Data before and after the government imposed control policies on 3 March 2020 were used to validate the model. Predictions for the disease's progression were provided together with the evaluation of the effectiveness of the mitigation measures implemented by the government and self-protective measures taken by the population. RESULTS: The model predicted that, if the government had continued to implement its strong control measures, then the scale of the pandemic would have decreased by 99% by the end of June 2020. Under the current relaxed policies, the model predicted that the scale of the pandemic will have decreased by 99% by 10 August 2020. The error between the model's predictions and actual data was less than 6.5%. CONCLUSIONS: Although the proposed model did not capture all of the effects of human behaviors and government actions, it was validated as a result of its time-dependent parameters. The model's accuracy indicates that it can be used by public health policymakers.

Dynamics of a COVID-19 Model with Nonlinear Incidence Rate, Quarantine, Media Effects and Number of Hospital Beds

In many countries the COVID-19 pandemic seems to witness second and third waves with dire consequences on human lives and economies. Given this situation the modeling of the transmission of the disease is still the subject of research with the ultimate goal of understanding the dynamics of the disease and assessing the efficacy of different mitigation strategies undertaken by the affected countries. We propose a mathematical model for COVID-19 transmission. The model is structured upon five classes: an individual can be susceptible, exposed, infectious, quarantined or removed. The model is based on a nonlinear incidence rate, takes into account the influence of media on public behavior, and assumes the recovery rate to be dependent on the hospital-beds to population ratio. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, stability analysis of the disease-free equilibrium (symmetry) and sensitivity analysis. We found that if the basic reproduction number is less than unity the system can exhibit Hopf and backward bifurcations for some range of parameters. Numerical simulations using parameter values fitted to Saudi Arabia are carried out to support the theoretical proofs and to analyze the effects of hospital-beds to population ratio, quarantine, and media effects on the predicted nonlinear behavior.

Bifurcation analysis of a SEIR epidemic system with governmental action and individual reaction.

In this paper, the dynamical behavior of a SEIR epidemic system that takes into account governmental action and individual reaction is investigated. The transmission rate takes into account the impact of governmental action modeled as a step function while the decreasing contacts among individuals responding to the severity of the pandemic is modeled as a decreasing exponential function. We show that the proposed model is capable of predicting Hopf bifurcation points for a wide range of physically realistic parameters for the COVID-19 disease. In this regard, the model predicts periodic behavior that emanates from one Hopf point. The model also predicts stable oscillations connecting two Hopf points. The effect of the different model parameters on the existence of such periodic behavior is numerically investigated. Useful diagrams are constructed that delineate the range of periodic behavior predicted by the model.