Related papers: On SIR-type epidemiological models and population …
This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…
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…
An SIR epidemic model with free boundary is investigated. This model describes the transmission of diseases. The behavior of positive solutions to a reaction-diffusion system in a radially symmetric domain is investigated. The existence and…
Many real networks are embedded in a metric space: the interactions among individuals depend on their spatial distances and usually take place among their nearest neighbors. In this paper, we introduce a modified…
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three…
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…
We investigate the SIR epidemic on a dynamic inhomogeneous Erd\H{o}s-R\'enyi random graph, in which vertices are of one of $k$ types and in which edges appear and disappear independently of each other. We establish a functional law of large…
Compartmental models of epidemics are widely used to forecast the effects of communicable diseases such as COVID-19 and to guide policy. Although it has long been known that such processes take place on social networks, the assumption of…
We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from…
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…
An epidemic model where disease transmission can occur either through global contacts or through local, nearest neighbor interactions is considered. The classical SIR--model describing the global interactions is extended by adding…
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…
Pandemics can cause immense disruption and damage to communities and societies. Thus far, modeling of pandemics has focused on either large-scale difference equation models like the SIR and the SEIR models, or detailed micro-level…
In real social networks, person-to-person interactions are known to be heterogeneous, which can affect the way a disease spreads through a population, reaches a tipping point in the fraction of infected individuals, and becomes an epidemic.…
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…
We study the impact of contact heterogeneity on epidemic dynamics. A system characterized by multiple susceptible populations is considered. The description of the spread of an infectious disease is obtained through the study of a system of…
Infectious disease epidemiologists routinely fit stochastic epidemic models to time series data to elucidate infectious disease dynamics, evaluate interventions, and forecast epidemic trajectories. To improve computational tractability,…
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…
The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common…
Recently the A/H1N1-2009 virus pandemic appeared in Mexico and in other nations. We present a study of this pandemic in the Mexican case using the SIR model to describe epidemics. This model is one of the simplest models but it has been a…