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We consider a space-time SI epidemic model with infection age-dependent infectivity and non-local infections constructed on a grid of the torus $\mathbb{T}^1 =(0, 1]^d$, where the individuals may migrate from node to another. The migration…
This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between…
We derive the master equations for the Susceptible-Infected (SI) model on general hypernetworks with~$N$-body interactions. We solve these equations exactly for infinite~$d$-regular hypernetworks, and obtain an explicit solution for the…
We consider the SIR model and study the first time the number of infected individuals begins to decrease and the first time this population is below a given threshold. We interpret these times as functions of the initial susceptible and…
In this study, a new and natural way of constructing a stochastic Susceptible-Infected-Susceptible (SIS) model is proposed. This approach is natural in the sense that the disease transmission rate, $\beta$, is substituted with a generic,…
The effect of the correlations in the diluteness pattern in the systems with non-integral dimensionality, on $\nu=\frac{4}{5}$ superdiffusion process is considered in this paper. These spatial correlations have proved to be very effective…
We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that,…
We prove a superdiffusive central limit theorem for the displacement of a test particle in the periodic Lorentz gas in the limit of large times $t$ and low scatterer densities (Boltzmann-Grad limit). The normalization factor is $\sqrt{t\log…
We determined the critical exponent $\nu$ of the scalar O(N) model with a strategy based on the definition of the correlation length in the infrared limit. The functional renormalization group treatment of the model shows that there is an…
The susceptible-exposed-infectious-susceptible (SEIS) model is well-known in mathematical epidemiology as a model of infection in which there is a latent period between the moment of infection and the onset of infectiousness. The…
We study the contact process on the configuration model with a power law degree distribution, when the exponent is smaller than or equal to two. We prove that the extinction time grows exponentially fast with the size of the graph and prove…
We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all…
Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the…
The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a $2^n$-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and,…
In models in statistical physics, the dynamics often slows down tremendously near the critical point. Usually, the correlation time $\tau$ at the critical point increases with system size $L$ in power-law fashion: $\tau \sim L^z$, which…
The appearance of the coronavirus (COVID-19) in late 2019 has dominated the news in the last few months as it developed into a pandemic. In many mathematics and physics classrooms, instructors are using the time series of the number of…
We develop theory to understand an intriguing property of diffusion models for image generation that we term critical windows. Empirically, it has been observed that there are narrow time intervals in sampling during which particular…
This paper studies an epidemic model with nonlocal dispersals. We focus on the influences of initial data and nonlocal dispersals on its spatial propagation. Here the initial data stand for the spatial concentrations of infectious agent and…
In this work we use the technique of the partial differential approximants to determine, from a pertubative supercritical series expansion for the ulimate survival probability, the critical line of the contact process model in one dimension…
This paper studies many-server limits for multi-server queues that have a phase-type service time distribution and allow for customer abandonment. The first set of limit theorems is for critically loaded $G/Ph/n+GI$ queues, where the…