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The SIR model is used extensively in the field of epidemiology, in particular, for the analysis of communal diseases. One problem with SIR and other existing models is that they are tailored to random or Erdos type networks since they do…
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 introduce a two-timescale SIRS-type model in which a fraction $\theta$ of infected individuals experiences a severe course of the disease, requiring hospitalization. During hospitalization, these individuals do not contribute to further…
The Susceptible-Infected-Recovered (SIR) epidemic model is extensively used for the study of the spread of infectious diseases. Even that the exact solution of the model can be obtained in an exact parametric form, in order to perform the…
Realistic human contact networks capable of spreading infectious disease, for example studied in social contact surveys, exhibit both significant degree heterogeneity and clustering, both of which greatly affect epidemic dynamics. To…
We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is comprised of a system of ordinary differential equations…
We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording…
Recent Covid-19 pandemic has demonstrated the need of efficient epidemic outbreak management. We study the optimal control problem of minimizing the fraction of infected population by applying vaccination and treatment control strategies,…
This work is concerned with epidemiological models defined on networks, which highlight the prominent role of the social contact network of a given population in the spread of infectious diseases. In particular, we address the modelling and…
Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two…
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the…
An SIRS epidemiological model for a vertically transmitted disease is discussed. We give a complete global analysis in terms of three explicit threshold parameters which respectively govern the existence and stability of an endemic…
Knowing which individuals can be more efficient in spreading a pathogen throughout a determinate environment is a fundamental question in disease control. Indeed, over the last years the spread of epidemic diseases and its relationship with…
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent p-coin tosses. Spatial variants of these models are proposed, in which finite…
Compartmental models are valuable tools for investigating infectious diseases. Researchers building such models typically begin with a simple structure where compartments correspond to individuals with different epidemiological statuses,…
This paper studies qualitative properties of solutions of nonlocal infectious SIR epidemic models (1.3)-(1.5), with the homogeneous Neumann boundary conditions, Dirichlet boundary conditions and free boundary, respectively. We first use the…
We analyze a finite volume scheme for nonlocal SIR model, which is a nonlocal reaction-diffusion system modeling an epidemic disease. We establish existence solutions to the finite volume scheme, and show that it converges to a weak…
Epidemiological models for the spread of pathogens in a population are usually only able to describe a single pathogen. This makes their application unrealistic in cases where multiple pathogens with similar symptoms are spreading…
A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…
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…