A study on COVID-19 transmission dynamics: stability analysis of SEIR model with Hopf bifurcation for effect of time delay

Within-host delay differential model for SARS-CoV-2 kinetics with saturated antiviral responses

The present study discussed a model to describe the SARS-CoV-2 viral kinetics in the presence of saturated antiviral responses. A discrete-time delay was introduced due to the time required for uninfected epithelial cells to activate a suitable antiviral response by generating immune cytokines and chemokines. We examined the system's stability at each equilibrium point. A threshold value was obtained for which the system switched from stability to instability via a Hopf bifurcation. The length of the time delay has been computed, for which the system has preserved its stability. Numerical results show that the system was stable for the faster antiviral responses of epithelial cells to the virus concentration, i.e., quick antiviral responses stabilized patients' bodies by neutralizing the virus. However, if the antiviral response of epithelial cells to the virus increased, the system became unstable, and the virus occupied the whole body, which caused patients' deaths.

A time-delayed model for the spread of COVID-19 with vaccination

A mathematical model is presented in this paper to investigate the effects of time delay in vaccine production on COVID-19 spread. The model is analyzed qualitatively and numerically. The qualitative analysis indicates that the system variables are non-negative, bounded, and biologically meaningful. Moreover, the model has produced two equilibrium points: the free equilibrium point, which can exist without conditions, and the endemic equilibrium point, which can exist if the control reproduction number, [Formula: see text], is not less than one. In addition, the local stability of the equilibrium points is investigated and agrees with the numerical analysis results. Finally, a sensitivity analysis is conducted for [Formula: see text]. In particular, we examine the effect of the vaccine's time delay, vaccine rate, and vaccine efficiency on the model dynamics.

Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness

This paper is focused on the design of optimal control strategies for COVID-19 and the model containing susceptible individuals with awareness of protection and susceptible individuals without awareness of protection is established. The goal of this paper is to minimize the number of infected people and susceptible individuals without protection awareness, and to increase the willingness of susceptible individuals to take protection measures. We conduct a qualitative analysis of this mathematical model. Based on the sensitivity analysis, the optimal control method is proposed, namely personal protective measures, vaccination and awareness raising programs. It is found that combining the three methods can minimize the number of infected people. Moreover, the introduction of awareness raising program in society will greatly reduce the existence of susceptible individuals without protection awareness. To evaluate the most cost-effective strategy we performed a cost-effectiveness analysis using the ICER method.

Dynamic Analysis of a COVID-19 Vaccination Model with a Positive Feedback Mechanism and Time-Delay

As the novel coronavirus pandemic has spread globally since 2019, most countries in the world are conducting vaccination campaigns. First, based on the traditional SIR infectious disease model, we introduce a positive feedback mechanism associated with the vaccination rate, and consider the time delay from antibody production to antibody disappearance after vaccination. We establish an UVaV model for COVID-19 vaccination with a positive feedback mechanism and time-delay. Next, we verify the existence of the equilibrium of the formulated model and analyze its stability. Then, we analyze the existence of the Hopf bifurcation, and use the multiple time scales method to derive the normal form of the Hopf bifurcation, further determining the direction of the Hopf bifurcation and the stability of the periodic solution of the bifurcation. Finally, we collect the parameter data of some countries and regions to determine the reasonable ranges of multiple parameters to ensure the authenticity of simulation results. Numerical simulations are carried out to verify the correctness of the theoretical results. We also give the critical time for controllable widespread antibody failure to provide a reference for strengthening vaccination time. Taking two groups of parameters as examples, the time of COVID-19 vaccine booster injection should be best controlled before 38.5 weeks and 35.3 weeks, respectively. In addition, study the impact of different expiration times on epidemic prevention and control effectiveness. We further explore the impact of changes in vaccination strategies on trends in epidemic prevention and control effectiveness. It could be concluded that, under the same epidemic vaccination strategy, the existence level of antibody is roughly the same, which is consistent with the reality.

Analysis of non-pharmaceutical interventions impacts on COVID-19 pandemic in Iran

The COVID-19 pandemic shows to have a huge impact on people's health and countries' infrastructures around the globe. Iran was one of the first countries that experienced the vast prevalence of the coronavirus outbreak. The Iranian authorities applied various non-pharmaceutical interventions to eradicate the epidemic in different periods. This study aims to investigate the effectiveness of non-pharmaceutical interventions in managing the current Coronavirus pandemic and to predict the next wave of infection in Iran. To achieve the research objective, the number of cases and deaths before and after the interventions was studied and the effective reproduction number of the infection was analyzed under various scenarios. The SEIR generic model was applied to capture the dynamic of the pandemic in Iran. To capture the effects of different interventions, the corresponding reproduction number was considered. Depending on how people are responsive to interventions, the effectiveness of each intervention has been investigated. Results show that the maximum number of the total of infected individuals will occur around the end of May and the start of June 2021. It is concluded that the outbreak could be smoothed if full lockdown and strict quarantine continue. The proposed modeling could be used as an assessment tool to evaluate the effects of different interventions in new outbreaks.

A review of mathematical model-based scenario analysis and interventions for COVID-19

Mathematical model-based analysis has proven its potential as a critical tool in the battle against COVID-19 by enabling better understanding of the disease transmission dynamics, deeper analysis of the cost-effectiveness of various scenarios, and more accurate forecast of the trends with and without interventions. However, due to the outpouring of information and disparity between reported mathematical models, there exists a need for a more concise and unified discussion pertaining to the mathematical modeling of COVID-19 to overcome related skepticism. Towards this goal, this paper presents a review of mathematical model-based scenario analysis and interventions for COVID-19 with the main objectives of (1) including a brief overview of the existing reviews on mathematical models, (2) providing an integrated framework to unify models, (3) investigating various mitigation strategies and model parameters that reflect the effect of interventions, (4) discussing different mathematical models used to conduct scenario-based analysis, and (5) surveying active control methods used to combat COVID-19.

Scenario analysis of COVID-19 transmission dynamics in Malaysia with the possibility of reinfection and limited medical resources scenarios

COVID-19 is a major health threat across the globe, which causes severe acute respiratory syndrome (SARS), and it is highly contagious with significant mortality. In this study, we conduct a scenario analysis for COVID-19 in Malaysia using a simple universality class of the SIR system and extensions thereof (i.e., the inclusion of temporary immunity through the reinfection problems and limited medical resources scenarios leads to the SIRS-type model). This system has been employed in order to provide further insights on the long-term outcomes of COVID-19 pandemic. As a case study, the COVID-19 transmission dynamics are investigated using daily confirmed cases in Malaysia, where some of the epidemiological parameters of this system are estimated based on the fitting of the model to real COVID-19 data released by the Ministry of Health Malaysia (MOH). We observe that this model is able to mimic the trend of infection trajectories of COVID-19 pandemic in Malaysia and it is possible for transmission dynamics to be influenced by the reinfection force and limited medical resources problems. A rebound effect in transmission could occur after several years and this situation depends on the intensity of reinfection force. Our analysis also depicts the existence of a critical value in reinfection threshold beyond which the infection dynamics persist and the COVID-19 outbreaks are rather hard to eradicate. Therefore, understanding the interplay between distinct epidemiological factors using mathematical modelling approaches could help to support authorities in making informed decisions so as to control the spread of this pandemic effectively.