Related papers: Continuous and discrete compartmental models for i…
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…
The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…
This study presents a neural network-enhanced approach to modeling disease spread dynamics over time and space. Neural networks are used to estimate time-varying parameters, with two calibration methods explored: Approximate Bayesian…
Viral kinetics have been extensively studied in the past through the use of spatially homogeneous ordinary differential equations describing the time evolution of the diseased state. However, spatial characteristics such as localized…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments…
Motivated by analogies between the spreading of human-to-human infections and of chemical processes, we develop a comprehensive model that accounts both for infection and for transport. In this analogy, the three different populations of…
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 COronaVIrus Disease 2019 (COVID-19) pandemic that has had the world in its grip from the beginning of 2020, has resulted in an unprecedented level of public interest and media attention on the field of mathematical epidemiology. Ever…
Coupling within-host infection dynamics with population-level transmission remains a major challenge in infectious disease modeling, especially for airborne pathogens with potential to spread indoor. The frequent emergence of such diseases…
In this work, we use a new approach to study the spread of an infectious disease. Indeed, we study a SIR epidemic model with variable infectivity, where the individuals are distributed over a compact subset $D$ of $\R^d$. We define…
The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the…
Understanding the dynamics of the spread of diseases within populations is critical for effective public health interventions. We extend the classical SIR model by incorporating additional complexities such as the introduction of a cure and…
Mathematical models of epidemic dynamics offer significant insight into predicting and controlling infectious diseases. The dynamics of a disease model generally follow a susceptible, infected, and recovered (SIR) model, with some standard…
We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…
A cellular automata model that describes as limit cases of his parameters the spread of contagious diseases modeled by systems of ordinary or partial differential equations is developed. Periodic features of the behavior of human settlement…
This paper gives an introduction to rule-based modelling applied to topics in infectious diseases. Rule-based models generalise reaction-based models with reagents that have internal state and may be bound together to form complexes, as in…
In this paper we present a model describing Susceptible-Infected-Susceptible (SIS) type epidemics spreading on a dynamic contact network with random link activation and deletion where link ac- tivation can be locally constrained. We use and…
Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between…
This paper analyses an SIRS-type model for infectious diseases with account for behavioural changes associated with the simultaneous spread of awareness in the population. Two types of awareness are included into the model: private…