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We develop a multiple compartment Susceptible-Infected-Recovered (SIR) model to analyze the spread of several infectious diseases through different geographic areas. Additionally, we propose a data-quality sensitive optimization framework…
The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
In this paper we analyze the effects of commuting and social inequalities for the epidemic development of the novel coronavirus (COVID-19). With this aim we consider a SEIRD (susceptible, exposed, infected, recovered and dead by disease)…
We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the tree vertex degree tends to infinity. We obtain the…
In this paper, we show how a dynamic population game can model the strategic interaction and migration decisions made by a large population of agents in response to epidemic prevalence. Specifically, we consider a modified…
Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node…
We introduce a general system of ordinary differential equations that includes some classical and recent models for the epidemic spread in a closed population without vital dynamic in a finite time horizon. The model is vectorial, in the…
This paper considers a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and varying total population. The interaction of the susceptible and infected people is describe by the…
To simplify mathematical models of disease spread, we often assume equal contact rates among hosts, but real-world scenarios differ. Network-based frameworks help capture these complexities and structural variations in actual systems. We…
Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and…
A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
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…
The exact analytical solution in closed form of a modified SIR system where recovered individuals are removed from the population is presented. In this dynamical system the populations $S(t)$ and $R(t)$ of susceptible and recovered…
We study the spread of stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school…
In their response to the COVID-19 outbreak, governments face the dilemma to balance public health and economy. Mobility plays a central role in this dilemma because the movement of people enables both economic activity and virus spread. We…
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…
The patterns of human mobility play a key role in the spreading of infectious diseases and thus represent a key ingredient of epidemic modeling and forecasting. Unfortunately, as the Covid-19 pandemic has dramatically highlighted, for the…
When estimating an effect of an action with a randomized or observational study, that study is often not a random sample of the desired target population. Instead, estimates from that study can be transported to the target population.…