On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility

A novel discrete-time COVID-19 epidemic model including the compartment of vaccinated individuals

Referring tothe study of epidemic mathematical models, this manuscript presents a noveldiscrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. By considering both the forward difference system and the backward difference system, some stability analyses of the disease-free fixed point are carried out.In particular, for the backward difference system a novel theorem is proved, which gives a condition for the disappearance of the pandemic when an inequality involving some epidemic parameters is satisfied. Finally, simulation results of the conceived discrete model are carried out, along with comparisons regarding the performances of both the forward difference system and the backward difference system.

Design a robust sliding mode controller based on the state and parameter estimation for the nonlinear epidemiological model of Covid-19

In this research, the challenging problem of Covid-19 mitigation is looked at from an engineering point of view. At first, the behavior of coronavirus in the Iranian and Russian societies is expressed by a set of ordinary differential equations. In the proposed model, the control input signals are vaccination, social distance and facial masks, and medical treatment. The unknown parameters of the system are estimated by long short-term memory (LSTM) algorithm. In the LSTM algorithm, the problem of long-term dependency is prevented. The uncertainty and measurement noises are inherent characteristics of epidemiological models. For this reason, an extended Kalman filter (EKF) is developed to estimate the state variables of the proposed model. In continuation, a robust sliding mode controller is designed to control the spread of coronavirus under vaccination, social distance and facial masks, and medical treatment. The stability of the closed-loop system is guaranteed by the Lyapunov theorems. The official confirmed data provided by the Iranian and Russian ministries of health are employed to simulate the proposed algorithms. It is understood from simulation results that global vaccination has the potential to create herd immunity in long term. Under the proposed controller, daily Covid-19 infections and deaths become less than 500 and 10 people, respectively.

A Study on COVID-19 Incidence in Europe through Two SEIR Epidemic Models Which Consider Mixed Contagions from Asymptomatic and Symptomatic Individuals

The impact of the SARS-CoV-2 (COVID-19) on the world has been partially controlled through different measures of social isolation and prophylaxis. Two new SEIR (Susceptible-Exposed-Infected-Recovered) models are proposed in order to describe this spread through different countries of Europe. In both models the infectivity of the asymptomatic period during the exposed stage of the disease will be taken into account. The different transmission rates of the SEIR models are calculated by considering the different locations and, more importantly, the lockdown measures implemented in each region. A new classification of these intervention measures will be set and their influence on the values of the transmission rates will be estimated through regression analysis.

On a Discrete SEIR Epidemic Model with Two-Doses Delayed Feedback Vaccination Control on the Susceptible

A new discrete susceptible-exposed-infectious-recovered (SEIR) epidemic model is presented subject to a feedback vaccination effort involving two doses. Both vaccination doses, which are subject to a non-necessarily identical effectiveness, are administrated by respecting a certain mutual delay interval, and their immunity effect is registered after a certain delay since the second dose. The delays and the efficacies of the doses are parameters, which can be fixed in the model for each concrete experimentation. The disease-free equilibrium point is characterized as well as its stability properties, while it is seen that no endemic equilibrium point exists. The exposed subpopulation is supposed to be infective eventually, under a distinct transmission rate of that of the infectious subpopulation. Some simulation examples are presented by using disease parameterizations of the COVID-19 pandemic under vaccination efforts requiring two doses.