Modeling the SARS-CoV-2 Omicron variant dynamics in the United States with booster dose vaccination and waning immunity.

We carried out a theoretical and numerical analysis for an epidemic model to analyze the dynamics of the SARS-CoV-2 Omicron variant and the impact of vaccination campaigns in the United States. The model proposed here includes asymptomatic and hospitalized compartments, vaccination with booster doses, and the waning of natural and vaccine-acquired immunity. We also consider the influence of face mask usage and efficiency. We found that enhancing booster doses and using N95 face masks are associated with a reduction in the number of new infections, hospitalizations and deaths. We highly recommend the use of surgical face masks as well, if usage of N95 is not a possibility due to the price range. Our simulations show that there might be two upcoming Omicron waves (in mid-2022 and late 2022), caused by natural and acquired immunity waning with respect to time. The magnitude of these waves will be 53% and 25% lower than the peak in January 2022, respectively. Hence, we recommend continuing to use face masks to decrease the peak of the upcoming COVID-19 waves.

Dynamics of a reaction-diffusion SIRS model with general incidence rate in a heterogeneous environment.

In this paper, we study a diffusive SIRS-type epidemic model with transfer from the infectious to the susceptible class. Our model includes a general nonlinear incidence rate and spatially heterogeneous diffusion coefficients. We compute the basic reproduction number R 0 of our model and establish the global stability of the disease-free steady state when R 0 < 1 . Furthermore, we study the uniform persistence when R 0 > 1 and perform a bifurcation analysis for a special case of our model. Some numerical simulations are presented to illustrate the dynamics of the solutions as the model parameters are varied.

An SEIARD epidemic model for COVID-19 in Mexico: Mathematical analysis and state-level forecast.

We propose an SEIARD mathematical model to investigate the current outbreak of coronavirus disease (COVID-19) in Mexico. Our model incorporates the asymptomatic infected individuals, who represent the majority of the infected population (with symptoms or not) and could play an important role in spreading the virus without any knowledge. We calculate the basic reproduction number (R 0) via the next-generation matrix method and estimate the per day infection, death and recovery rates. The local stability of the disease-free equilibrium is established in terms of R 0. A sensibility analysis is performed to determine the relative importance of the model parameters to the disease transmission. We calibrate the parameters of the SEIARD model to the reported number of infected cases, fatalities and recovered cases for several states in Mexico by minimizing the sum of squared errors and attempt to forecast the evolution of the outbreak until November 2020.