Related papers: Basic concepts for the Kermack and McKendrick mode…
We develop a stochastic epidemic model progressing over dynamic networks, where infection rates are heterogeneous and may vary with individual-level covariates. The joint dynamics are modeled as a continuous-time Markov chain such that…
We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals…
Infectious disease outbreaks have precipitated a profusion of mathematical models. Epidemic curves predicted by these models are typically qualitatively similar, despite distinct model assumptions, but there is no theoretical explanation…
We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a…
The recent COVID-19 pandemic has shown that when the reproduction number is high and there are no proper measurements in place, the number of infected people can increase dramatically in a short time, producing a phenomenon that many…
A network epidemic model is studied. The underlying social network has two different types of group structures, households and workplaces, such that each individual belongs to exactly one household and one workplace. The random network is…
This is work in progress. We make it accessible hoping that people might find the idea useful. We propose a discrete, recursive 5-compartment model for the spread of epidemics, which we call {\em SEPIR-model}. Under mild assumptions which…
Many real networks are not isolated from each other but form networks of networks, often interrelated in non trivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…
The results of Kermack-McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of epidemic, systematically. The basic goal is to capture the effects of…
The complex interplay between population movements in space and non-homogeneous mixing patterns have so far hindered the fundamental understanding of the conditions for spatial invasion through a general theoretical framework. To address…
Network--based epidemic models that account for heterogeneous contact patterns are extensively used to predict and control the diffusion of infectious diseases. We use census and survey data to reconstruct a geo--referenced and…
In this paper, we introduce and study an age-structured epidemiological compartment model and its respective problem, applied but not limited to the COVID-19 pandemic, in order to investigate the role of the age of the individuals in the…
This study proposes a nonhomogeneous birth--death model which captures the dynamics of a directly transmitted infectious disease. Our model accounts for an important aspect of observed epidemic data in which only symptomatic infecteds are…
We consider a multi-species reaction-diffusion system that arises in epidemiology to describe the spread of several strains, or variants, of a disease in a population. Our model is a natural spatial, multi-species, extension of the…
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight…
Drug resistance and strong contacts actually play crucial roles in epidemic spread in complex systems. Nevertheless, neither theoretical model or methodology is proposed to address this. We thus consider an edge-based epidemic spread model…
Motivated by chemical reaction rules, we introduce a rule-based epidemiological framework for the systematic mathematical modelling of future pandemics. Here we stress that we do not have a specific model in mind, but a whole collection of…
Infection can spread easily on networks with heterogeneous degree distribution. Here, we considered targeted immunization on such networks, wherein a fraction of individuals with the highest connectivity are immunized. To quantify the…
Metapopulation models are commonly used in ecology, evolution, and epidemiology. These models usually entail homogeneity assumptions within patches and study networks of migration between patches to generate insights into conservation of…