Related papers: Critical asymptotic behaviour in the SIR model
We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions…
Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by…
An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed and several…
Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the…
The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modeling and forecasting. The SIR (Susceptible-Infected-Removed) model is a…
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…
Age structure is incorporated in many types of epidemic model. Often it is convenient to assume that such models converge to early asymptotic behaviour quickly, before the susceptible population has been appreciably depleted. We make use of…
An SEIRS epidemic with disease fatalities is introduced in a growing population (modelled as a super-critical linear birth and death process). The study of the initial phase of the epidemic is stochastic, while the analysis of the major…
For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix $R_{mn}$, whose elements converge to two constants. This allows for an effective extrapolation of the…
We study the critical effect of an intermittent social distancing strategy on the propagation of epidemics in adaptive complex networks. We characterize the effect of our strategy in the framework of the susceptible-infected-recovered…
We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number $\mathcal{R}_0$ of the pathogen can be defined in that…
The outcome of SIR epidemics with heterogeneous infective lifetimes, or heterogeneous susceptibilities, can be mapped onto a directed percolation process on the underlying contact network. In this paper we study SIR models where…
We consider an SIR-type (Susceptible $\to$ Infected $\to$ Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model…
This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total…
We define and study an open stochastic SIR (Susceptible -- Infected -- Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same…
This paper revisits a longstanding problem of interest concerning the distributed control of an epidemic process on human contact networks. Due to the stochastic nature and combinatorial complexity of the problem, finding optimal policies…
Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been…
We adapt the article of Forien, Pang, Pardoux and Zotsa: Arxiv preprint Arxiv2210.04667(2022), on epidemic models with varying infectivity and waning immunity, to incorporate the memory of the last infection. To this end, we introduce a…
When the body gets infected by a pathogen the immune system develops pathogen-specific immunity. Induced immunity decays in time and years after recovery the host might become susceptible again. Exposure to the pathogen in the environment…
Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by…