We consider a Susceptible-Infective-Removed (SIR) stochastic epidemic model in which the infection rate is of the form βN⁻¹X(t)Y(t)(α). It is demonstrated that both the threshold behaviour of this model and the behaviour of the corresponding deterministic model differ markedly from the standard SIR model (i.e. α=1). Methods of statistical inference for this model are described, given outbreak d...

Mathematical models of the epidemic have been developed and researched to predict development COVID-19 coronavirus on thebasis information technology for optimizing complex dynamic systems. epidemics SIR, SIRS, SEIR, SIS, MSEIR in theform nonlinear systems differential equations are considered analysis use mathematical research ofepidemic is carried out. Based statistics Kharkiv region, theinit...

We consider a heterogeneously mixing SIR stochastic epidemic process in populations described by a general graph. Likelihood theory is developed to facilitate statistic inference for the parameters of the model under complete observation. We show that these estimators are asymptotically Gaussian unbiased estimates by using a martingale central limit theorem. Keywords—statistic inference, maximu...

A brief introduction to the formulation of various types of stochastic epidemic models is presented based on the well-known deterministic SIS and SIR epidemic models. Three different types of stochastic model formulations are discussed: discrete time Markov chain, continuous time Markov chain and stochastic differential equations. Properties unique to the stochastic models are presented: probab...

Compartmental mathematical models are frequently used in epidemiology. These types of rely on some assumptions, such as the homogeneity society and equal contact ratio everyone, to model real-life events mathematically. In real life, due heterogeneous nature social network that constitutes society, rates times individuals vary. sudden new epidemics, solutions vaccines slow down or end epidemics...