# Recent Advances in Epidemic Modeling: Non-Markov Stochastic Models and their Scaling Limits

@inproceedings{Forien2021RecentAI, title={Recent Advances in Epidemic Modeling: Non-Markov Stochastic Models and their Scaling Limits}, author={R. Forien and G. Pang and {\'E}. Pardoux}, year={2021} }

In this survey paper, we review the recent advances in individual based non–Markovian epidemic models. They include epidemic models with a constant infectivity rate, varying infectivity rate or infection-age dependent infectivity, infection-age recovery rate (or equivalently, general law of infectious period), as well as varying susceptibility/immunity. We focus on the scaling limits with a large population, functional law of large numbers (FLLN) and functional central limit theorems (FCLT… Expand

#### References

SHOWING 1-10 OF 95 REFERENCES

Functional central limit theorems for epidemic models with varying infectivity

- Mathematics
- 2020

In this paper, we prove functional central limit theorems (FCLTs) for a stochastic epidemic model with varying infectivity and general infectious periods recently introduced in Forien, Pang and… Expand

Functional law of large numbers and PDEs for epidemic models with infection-age dependent infectivity

- Mathematics
- 2021

We study epidemic models where the infectivity of each individual is a random function of the infection age (the elapsed time of infection). To describe the epidemic evolution dynamics, we use a… Expand

Epidemic models with varying infectivity

- Mathematics
- 2020

We introduce an epidemic model with varying infectivity and general exposed and infectious periods, where the infectivity of each individual is a random function of the elapsed time since infection,… Expand

Stochastic epidemics in a homogeneous community

- Mathematics
- 2018

These notes describe stochastic epidemics in a homogenous community. Our main concern is stochastic compartmental models (i.e. models where each individual belongs to a compartment, which stands for… Expand

Multi-patch epidemic models with general exposed infectious periods

- Mathematics
- 2020

We study multi-patch epidemic models where individuals may migrate from one patch to another in either of the susceptible, exposed/latent, infectious and recovered states. We assume that infections… Expand

Moderate deviations and extinction of an epidemic

- Mathematics
- 2020

Consider an epidemic model with a constant flux of susceptibles, in a situation where the corresponding deterministic epidemic model has a unique stable endemic equilibrium. For the associated… Expand

SIR epidemic models with general infectious period distribution

- Mathematics
- 2014

We show how epidemics in which individuals’ infectious periods are not necessarily exponentially distributed may be naturally modelled as piecewise deterministic Markov processes. For the standard… Expand

Large deviations for infectious diseases models

- Mathematics
- 2018

We study large deviations of a Poisson driven system of stochastic differential equations modeling the propagation of an infectious disease in a large population, considered as a small random… Expand

Law of large numbers for the SIR epidemic on a random graph with given degrees

- Mathematics, Computer Science
- Random Struct. Algorithms
- 2014

The main result is that, conditional on a large outbreak, the evolutions of certain quantities of interest, such as the fraction of infective vertices, converge to deterministic functions of time. Expand

Limit theorems for age and density dependent stochastic population models

- Mathematics
- 1975

SummaryConsider a population consisting of m different types of individuals living in a fixed region with area A. We construct a stochastic population model in which the death rate is affected by the… Expand