Related papers: Theory of Infectious Diseases with Testing and Tes…
In this study, we present a new epidemiological model, with contamination from confirmed and unreported. We also compute equilibria and study their stability without intervention strategies. Optimal control theory has proven to be a…
A significant proportion of the infections driving the current {SARS-CoV-2} pandemic are transmitted asymptomatically. Here we introduce and study a simple epidemic model with separate compartments comprising asymptomatic and symptomatic…
At the time of writing, the ongoing COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), had already resulted in more than thirty-two million cases infected and more than one million deaths worldwide.…
To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the…
We consider the SEIRS compartment epidemiology model suitable for predicting the evolution of the COVID-19 pandemy in the extreme limiting case of no acquired immunity. The disease-free and endemic fixed points are found and their stability…
Assuming a general distribution for the sojourn time in the in- fectious class, we consider an SIS type epidemic model formulated as a scalar integral equation. We prove that the endemic equilibrium of the model is globally asymptotically…
We investigate the global dynamics of a renewal-type epidemic model with variable susceptibility. We show that in this extended model there exists a unique endemic equilibrium and prove that it is globally asymptotically stable when $R_0 >…
A new epidemic model for Covid-19 has been constructed and simulated for eight US states. The coefficients for this model, based on seven coupled differential equations, are carefully evaluated against recorded data on cases and deaths.…
This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the…
We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also…
The COVID-19 crisis highlighted the importance of non-medical interventions, such as testing and isolation of infected individuals, in the control of epidemics. Here, we show how to minimize testing needs while maintaining the number of…
In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated…
We study an S--I type epidemic model in an age-structured population, with mortality due to the disease. A threshold quantity is found that controls the stability of the disease-free equilibrium and guarantees the existence of an endemic…
In the recent COVID-19 pandemic we assisted at a sequence of epidemic waves intertwined by anomalous fade-outs with periods of low but persistent epidemic prevalence. These long-living epidemic states complicate epidemic control and…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…
In this paper we consider the stability of a class of deterministic and stochastic SEIRS epidemic models with delay. Indeed, we assume that the transmission rate could be stochastic and the presence of a latency period of $r$ consecutive…
Transmission dynamics of infectious diseases are often studied using compartmental mathematical models, which are commonly represented as systems of autonomous ordinary differential equations. A key step in the analysis of such models is to…
We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the $n$-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread…
We consider the SEIRS epidemiology model with such features of the COVID-19 outbreak as: abundance of unidentified infected individuals, limited time of immunity and a possibility of vaccination. The control of the pandemic dynamics is…
This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral…