Related papers: Epidemic Extinction in a Continuous SIRS Model wit…
We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted…
Understanding dynamics of an infectious disease helps in designing appropriate strategies for containing its spread in a population. Recent mathematical models are aimed at studying dynamics of some specific types of infectious diseases. In…
In this paper, we consider a reaction-diffusion-advection SIS epidemic model with saturated incidence rate and linear source. We study the uniform bounds of parabolic system and some asymptotic behavior of the basic reproduction number…
The primary goal of this research is to investigate the impact of delay on the dynamics of the Susceptible-Exposed-Infected-Recovered-Death and Susceptible (SEIRDS) model, to which we add a stochastic term to account for uncertainty in…
Time varying susceptibility of host at individual level due to waning and boosting immunity is known to induce rich long-term behavior of disease transmission dynamics. Meanwhile, the impact of the time varying heterogeneity of host…
This paper considers the susceptible-infected-susceptible (SIS) epidemic model with an underlying network structure among subpopulations and focuses on the effect of social distancing to regulate the epidemic level. We demonstrate that if…
Branching processes are widely used to model evolutionary and population dynamics as well as the spread of infectious diseases. To characterize the dynamics of their growth or spread, the basic reproduction number $R_0$ has received…
We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…
A model of reactive social distancing in epidemics is proposed, in which the infection rate changes with the number infected. The final-size equation for the total number that the epidemic will infect can be derived analytically, as can the…
We study supercritical spatial SIR epidemics on $\mathbb{Z}^2\times \{1,2,\ldots, N\}$, where each site in $\mathbb{Z}^2$ represents a village and $N$ stands for the village size. We establish several key asymptotic results as $N\to\infty$.…
This study presents a comprehensive analysis of a two-patch, two-life stage SI model without recovery from infection, focusing on the dynamics of disease spread and host population viability in natural populations. The model, inspired by…
Transmission rates in epidemic outbreaks may vary over time depending on the societal response. Non-pharmacological mitigation strategies such as social distancing and the adoption of protective equipment aim precisely at reducing…
Numerous elements drive the spread of infectious diseases in complex real-world networks. Of particular interest is social behaviors that evolve in tandem with the spread of disease. Moreover, recent studies highlight the importance of…
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We…
This article presents a comprehensive study of the continuous McKendrick model, which serves as a foundational framework in population dynamics and epidemiology. The model is formulated through partial differential equations that describe…
We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition…
Infectious disease transmission in human populations has a complex two-way interaction with changes in host behaviour. It is increasingly recognised that incorporating adaptive behavioural change into epidemic models is important for…
This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…
The Susceptible-Infected-Susceptible (SIS) model is a widely used model for the spread of information and infectious diseases, particularly non-immunizing ones, on a graph. Given a highly contagious disease, a natural question is how to…
In this paper, we investigate a parabolic-ODE SIS epidemic model with no-flux boundary conditions in a heterogeneous environment. The model incorporates a saturated infection mechanism \({SI}/(m(x) + S + I)\) with \(m \geq,\,\not\equiv 0\).…