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

Abstract

A new discrete Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is proposed, and its properties of non-negativity and (both local and global) asymptotic stability of the solution sequence vector on the first orthant of the state-space are discussed. The calculation of the disease-free and the endemic equilibrium points is also performed. The model has the following main characteristics: (a) the exposed subpopulation is infective, as it is the infectious one, but their respective transmission rates may be distinct; (b) a feedback vaccination control law on the Susceptible is incorporated; and (c) the model is subject to delayed partial re-susceptibility in the sense that a partial immunity loss in the recovered individuals happens after a certain delay. In this way, a portion of formerly recovered individuals along a range of previous samples is incorporated again to the susceptible subpopulation. The rate of loss of partial immunity of the considered range of previous samples may be, in general, distinct for the various samples. It is found that the endemic equilibrium point is not reachable in the transmission rate range of values, which makes the disease-free one to be globally asymptotically stable. The critical transmission rate which confers to only one of the equilibrium points the property of being asymptotically stable (respectively below or beyond its value) is linked to the unity basic reproduction number and makes both equilibrium points to be coincident. In parallel, the endemic equilibrium point is reachable and globally asymptotically stable in the range for which the disease-free equilibrium point is unstable. It is also discussed the relevance of both the vaccination effort and the re-susceptibility level in the modification of the disease-free equilibrium point compared to its reached component values in their absence. The influences of the limit control gain and equilibrium re-susceptibility level in the reached endemic state are also explicitly made viewable for their interpretation from the endemic equilibrium components. Some simulation examples are tested and discussed by using disease parameterizations of COVID-19.

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

“…This section contains some simulation examples devoted to study the application of the two-doses vaccination to counteract the spread of the COVID-19 pandemic. To this end the case of Italy borrowed from [45], where the discrete-model dynamics is confronted with actual data from Italy, will be considered. Thus, we have a discrete-time COVID-19 model serving as benchmark for the vaccination control.…”

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

“…This is not very surprising since former studies indicate that a small residual permanent nonzero susceptible population can exist even if the infection asymptotically extinguishes, implying that not all the population becomes asymptotically recovered. See, for instance, [51,52]. The reason is that the coefficient sequence of Equation ( 1) of general term a i = 1 − (β…”

Simulating Immunization Campaigns and Vaccine Protection Against COVID-19 Pandemic in Brazil

“…An alternative SIR-type model covering impulsive vaccination strategies has been discussed by Etxeberria-Etxaniz et al [24], while the mass vaccination in Greece was analyzed by Rachaniotis et al [25]. The vaccination was also considered as part of a feedback immunization control rule in the model studied by De la Sen et al [26], while Mak et al [27] assumed a twodose vaccine model to explore vaccine rollout policies.…”