Toward the Impact of Non-pharmaceutical Interventions and Vaccination on the COVID-19 Pandemic With Time-Dependent SEIR Model

Abstract

The outbreak of COVID-19, caused by the SARS-CoV-2 coronavirus, has been declared a pandemic by the World Health Organization (WHO) in March, 2020 and rapidly spread to over 210 countries and territories around the world. By December 24, there are over 77M cumulative confirmed cases with more than 1.72M deaths worldwide. To mathematically describe the dynamic of the COVID-19 pandemic, we propose a time-dependent SEIR model considering the incubation period. Furthermore, we take immunity, reinfection, and vaccination into account and propose the SEVIS model. Unlike the classic SIR based models with constant parameters, our dynamic models not only predicts the number of cases, but also monitors the trajectories of changing parameters, such as transmission rate, recovery rate, and the basic reproduction number. Tracking these parameters, we observe the significant decrease in the transmission rate in the U.S. after the authority announced a series of orders aiming to prevent the spread of the virus, such as closing non-essential businesses and lockdown restrictions. Months later, as restrictions being gradually lifted, we notice a new surge of infection emerges as the transmission rates show increasing trends in some states. Using our epidemiology models, people can track, timely monitor, and predict the COVID-19 pandemic with precision. To illustrate and validate our model, we use the national level data (the U.S.) and the state level data (New York and North Dakota), and the resulting relative prediction errors for the infected group and recovered group are mostly lower than 0.5%. We also simulate the long-term development of the pandemic based on our proposed models to explore when the crisis will end under certain conditions.

Measuring the impact of COVID-19 vaccination and immunity waning: a modelling study for Portugal

“…Hence, considering the present setting, our results suggest that solely vaccinating the targeted age-groups might not be sufficient to bring the Rt bellow one and prevent epidemic disease spread, even considering high vaccination coverage rates. These results are also in accordance with other Portuguese modelling studies [10,31] and also international studies [11,12,13,14] which also present epidemic spread in the presence of vaccination. Consequently the Portuguese government recently decided to vaccinate those between 5 to 11 years old, which according to our results would further reduce disease transmission and could even control disease spread in the worst hypothetical scenario considered (R D 0 = 5 and no NPIs) if vaccine effectiveness is high (> 95%).…”

COVID-19 Waves: Variant Dynamics and Control

“…The minimization problem of ( 11) is constrained to the coupled dynamics of the nonlinear SI 2 Q 2 R 2 V D equations ( 1)-( 9), that cannot be integrated analytically, hence neither could the gradients of the cost function be computed. Therefore, a derivative free stochastic optimization technique of Nelder and Mead 21 is adapted to solve the nonlinear optimization problem, the algorithm follows: (11).…”

“…A simple SIR model plus exposed/E state with prophylactic and therapeutic interventions was considered to analyze the stability of the pandemic 9 . A similar model was simulated with stochastic transmission and recovery rates 10 and analyzed in a discrete time setting with auto-regressive transmission rate 11 .…”

An extended SEIARD model for COVID-19 vaccination in Mexico: analysis and forecast

“…The stability analysis of an SEIR model with prophylactic and therapeutic vaccines was performed in [38]. In [20], the effect of immunity, vaccination, and reinfection with changing parameters was analysed using an SEVIS model, while in [13] an SIQRD model was used to simulate several scenarios of vaccine delivery in Indonesia.…”