Related papers: How many outbreaks before an epidemic?
We propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of super-spreaders individuals. We compute the basic reproduction number threshold, we study the local stability…
Motile organisms can form stable agglomerates such as cities or colonies. In the outbreak of a highly contagious disease, the control of large-scale epidemic spread depends on factors like the number and size of agglomerates, travel rate…
Motivated by the rapid spread of COVID-19 all across the globe, we have performed simulations of a system dynamic epidemic spread model in different possible situations. The simulation, not only captures the model dynamic of the spread of…
For a given, arbitrary graph, what is the epidemic threshold? That is, under what conditions will a virus result in an epidemic? We provide the super-model theorem, which generalizes older results in two important, orthogonal dimensions.…
We study the susceptible-infective-recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant…
The suggestion by K.L. Cooke (1967) that infected individuals become infective if they are exposed often enough for a natural disease resistance to be overcome is built into a Kermack-McKendrick type epidemic model with infectivity age.…
Classical epidemiological models assume homogeneous populations. There have been important extensions to model heterogeneous populations, when the identity of the sub-populations is known, such as age group or geographical location. Here,…
Risk-driven behavior provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of heterogeneity in the…
Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, so that fluctuations around their average are…
The COVID-19 pandemic led to widespread interest in epidemiological models. In this context the role of vaccination in influencing the spreading of the disease is of particular interest. There has also been a lot of debate on the role of…
Pandemic control measures like lock-down, restrictions on restaurants and gatherings, social-distancing have shown to be effective in curtailing the spread of COVID-19. However, their sustained enforcement has negative economic effects. To…
Extreme public health interventions play a critical role in mitigating the local and global prevalence and pandemic potential of COVID-19. Here, we use population size for pathogen transmission to measure the intensity of public health…
Consider a random graph, having a pre-specified degree distribution F but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose one individual in the community is externally…
The basic reproductive number -- $R_0$ -- is one of the most common and most commonly misapplied numbers in public health. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that…
We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic…
A compartmental epidemic model is proposed to predict the Covid-19 virus spread. It considers: both detected and undetected infected populations, medical quarantine and social sequestration, release from sequestration, plus possible…
The review is devoted to analysis of mathematical models used for describing epidemic processes. A main focus is done on the models that are based on partial differential equations (PDEs), especially those that were developed and used for…
We present a finite-size scaling theory of a contact process with permanent immunity on uncorrelated scale-free networks. We model an epidemic outbreak by an analog of the susceptible-infected-removed model where an infected individual…
Epidemic models are always simplifications of real world epidemics. Which real world features to include, and which simplifications to make, depend both on the disease of interest and on the purpose of the modelling. In the present paper we…
The interplay of biological, social, structural and random factors makes disease forecasting extraordinarily complex. The course of an epidemic exhibits average growth dynamics determined by features of the pathogen and the population, yet…