Related papers: Basic concepts for the Kermack and McKendrick mode…
Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the…
In the recent COVID-19 pandemic we assisted at a sequence of epidemic waves intertwined by anomalous fade-outs with periods of low but persistent epidemic prevalence. These long-living epidemic states complicate epidemic control and…
In this paper, we first propose a diffusive pathogen infection model with general incidence rate which incorporates cell-to-cell transmission. By applying the theory of monotone dynamical systems, we prove that the model admits the global…
In the first part of this paper, we review old and new results about the influence of host population heterogeneity on (various characteristics of) epidemic outbreaks. In the second part we highlight a modelling issue that so far has…
Human to human transmissible infectious diseases spread in a population using human interactions as its transmission vector. The early stages of such an outbreak can be modeled by a graph whose edges encode these interactions between…
Epidemiological processes are studied within a recently proposed hierarchical network model using the susceptible-infected-refractory dynamics of an epidemic. Within the network model, a population may be characterized by $H$ independent…
We will study a mathematical model of the human immunodeficiency virus (HIV) infection in the presence of combination therapy that includes within-host infectious dynamics. The deterministic model requires us to analyze asymptotic stability…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…
This paper presents a detailed mathematical investigation into the dynamics of COVID-19 infections through extended Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological models. By…
We introduce an extension to Kermack and McKendrick's classic susceptible-infected-recovered (SIR) model in epidemiology, whose underlying mechanism of infection consists of individuals attending randomly generated social gatherings. This…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…
In contrast to the many theoretical studies on the transmission of human-mosquitoes malaria infection, few studies have considered a multiple structure model formulations including (i) the chronological age of humans and mosquitoes…
A model of interacting agents, following plausible behavioral rules into a world where the Covid-19 epidemic is affecting the actions of everyone. The model works with (i) infected agents categorized as symptomatic or asymptomatic and (ii)…
The paper presents an algorithm for syndromic surveillance of an epidemic outbreak formulated in the context of stochastic nonlinear filtering. The dynamics of the epidemic is modeled using a generalized compartmental epidemiological model…
The abrupt outbreak and transmission of biological diseases has always been a long-time concern of humankind. For long, mathematical modeling has served as a simple and yet efficient tool to investigate, predict, and control spread of…
We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold…
This paper presents a compact pairwise model that describes the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian…
We present a model of contagion that unifies and generalizes existing models of the spread of social influences and micro-organismal infections. Our model incorporates individual memory of exposure to a contagious entity (e.g., a rumor or…
We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations…
During the COVID-19 pandemic, different countries, regions, and communities constructed various epidemic models to evaluate spreading behaviors and assist in making mitigation policies. Model uncertainties, introduced by complex…