Effects of vaccination on mitigating COVID-19 outbreaks: a conceptual modeling approach.

This paper is devoted to investigating the impact of vaccination on mitigating COVID-19 outbreaks. In this work, we propose a compartmental epidemic ordinary differential equation model, which extends the previous so-called SEIRD model [1,2,3,4] by incorporating the birth and death of the population, disease-induced mortality and waning immunity, and adding a vaccinated compartment to account for vaccination. Firstly, we perform a mathematical analysis for this model in a special case where the disease transmission is homogeneous and vaccination program is periodic in time. In particular, we define the basic reproduction number $ \mathcal{R}_0 $ for this system and establish a threshold type of result on the global dynamics in terms of $ \mathcal{R}_0 $. Secondly, we fit our model into multiple COVID-19 waves in four locations including Hong Kong, Singapore, Japan, and South Korea and then forecast the trend of COVID-19 by the end of 2022. Finally, we study the effects of vaccination again the ongoing pandemic by numerically computing the basic reproduction number $ \mathcal{R}_0 $ under different vaccination programs. Our findings indicate that the fourth dose among the high-risk group is likely needed by the end of the year.

Analysis of a COVID-19 Epidemic Model with Seasonality.

The statistics of COVID-19 cases exhibits seasonal fluctuations in many countries. In this paper, we propose a COVID-19 epidemic model with seasonality and define the basic reproduction number [Formula: see text] for the disease transmission. It is proved that the disease-free equilibrium is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and there exists at least one positive periodic solution when [Formula: see text]. Numerically, we observe that there is a globally asymptotically stable positive periodic solution in the case of [Formula: see text]. Further, we conduct a case study of the COVID-19 transmission in the USA by using statistical data.

Global stability and optimal control for a COVID-19 model with vaccination and isolation delays.

COVID-19 pandemic remains serious around the world and causes huge deaths and economic losses. To investigate the effect of vaccination and isolation delays on the transmission of COVID-19, we propose a mathematical model of COVID-19 transmission with vaccination and isolation delays. The basic reproduction number is computed, and the global dynamics of the model are proved. When R 0 < 1 , the disease-free equilibrium is globally asymptotically stable. The unique endemic equilibrium is globally asymptotically stable if R 0 > 1 . Based on the public information, parameter values are estimated, and sensitivity analysis is carried out by the partial rank correlation coefficients (PRCCs) and the extended version of the Fourier amplitude sensitivity test (eFAST). Our results suggest that the isolation rates of asymptomatic and symptomatic infectious individuals have a significant impact on the transmission of COVID-19. When the COVID-19 is epidemic, the optimal control strategies of our model with vaccination and isolation delays are analyzed. Under the limited resource with constant and time-varying isolation rates, we find that the optimal isolation rates may minimize the cumulative number of infected individuals and the cost of disease control, and effectively contain the transmission of COVID-19. Our study may help public health to prevent and control the COVID-19 spread.