Related papers: A non-standard numerical scheme for an age-of-infe…
Ordinary differential equations (ODE) are a popular tool to model the spread of infectious diseases, yet they implicitly assume an exponential distribution to describe the flow from one infection state to another. However, scientific…
We consider compartmental models in epidemiology. For the study of the divergence of the stochastic model from its corresponding deterministic limit (i.e., the solution of an ODE) for long time horizon, a large deviations principle suggests…
A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment…
We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a…
We analyse the infection-age-dependent SIR model from a numerical point of view. First, we present an algorithm for calculating the solution the infection-age-structured SIR model without demography of the background host. Second, we…
We study an individual-based stochastic spatial epidemic model where the number of locations and the number of individuals at each location both grow to infinity. Each individual is associated with a random infection-age dependent…
A new age-structured diffusive model for the mathematical modelling of epidemics is suggested. The model can be considered as a generalization of two models suggested earlier for the same purposes. The Lie symmetry classification of the…
We present EPITIME (EPidemic Integral models TIMe profile Explorer), a computational framework for the simulation of two classes of integral epidemic models: an age of infection model and an information dependent behavioural model. The…
Age-dependent dynamics is an important characteristic of many infectious diseases. Age-group epidemic models describe the infection dynamics in different age-groups by allowing to set distinct parameter values for each. However, such models…
Mathematical modeling is one of the key factors of the effective control of newly found infectious diseases, such as COVID-19. Our knowledge about the parameters and the course of the infection is highly limited in the beginning of the…
In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of…
In this article a space-dependent epidemic model equipped with a constant latency period is examined. We construct a delay partial integro-differential equation and show that its solution possesses some biologically reasonable features. We…
This paper introduces a nonstandard finite difference (NSFD) approach to a reaction-diffusion SEIQR epidemiological model, which captures the spatiotemporal dynamics of infectious disease transmission. Formulated as a system of semilinear…
Inspired by the paper Greenhalgh et al. [5] we investigate a class of two dimensional stochastic differential equations related to susceptible-infected-susceptible epidemic models with demographic stochasticity. While preserving the key…
In this work we examine the properties of a recently described ordinary differential equation that relates the age-specific prevalence of a chronic disease with the incidence and mortalities of the diseased and healthy persons. The equation…
We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…
We formulate a general age-of-infection epidemic model with two pathways: the symptomatic infections and the asymptomatic infections. We then calculate the basic reproduction number $\mathcal{R}_0$ and establish the final size relation. It…
In infectious disease modelling, the expected time from endemicity to extinction (of infection) may be analysed via WKB approximation, a method with origins in mathematical physics. The method is very general, but its uptake to date may…