Exploiting the power of the expectation operator and indicator (or Bernoulli) random variables, we present the exact governing equations for both the SIR and SIS epidemic models on networks. Although SIR and SIS are basic epidemic models, deductions from their exact stochastic equations without making approximations (such as the common mean-field approximation) are scarce. An exact analytic sol...

In this article, we study the fractional SIR epidemic model with Atangana–Baleanu–Caputo operator. We explore properties and applicability of ZZ transformation on operator as transform derivative. This is an application two power methods. obtain a special solution homotopy perturbation method (HPM) combined scheme; then present problem existence solution, also apply new to solving ABC The solut...

This work addresses the spread of a disease within an urban system, defined as a network of interconnected cities. The first step consists of comparing two different approaches: a macroscopic one, based on a system of coupled Ordinary Differential Equations (ODE) Susceptible-Infected-Recovered (SIR) systems exploiting populations on nodes and flows on edges (so-called metapopulational model), a...

The detection of an epidemic source or the patient zero is an important practical problem that can help in developing the epidemic control strategies. In this paper, we study the statistical inference problem of detecting the source of epidemics from a snapshot of a contagion spreading process at some time on an arbitrary network structure. By using exact analytic calculations and Monte Carlo s...

In the present paper, SIR model tracks numbers of susceptible, infected and recovered individuals during an epidemic with help ordinary differential equations (ODE). First, we give formulation our phenomena. Secondly, a fully discrete difference scheme is derived for model.At end this aper, simulation results model. A comparison obtained numerical both models performed in absence exact solution.

In this paper, we prove a functional central limit theorem (FCLT) for stochastic epidemic model with varying infectivity and general infectious periods recently introduced in R. Forien et al. [Epidemic models infectivity, SIAM J. Appl. Math. 81 (2021), pp. 1893–1930]. The process (total force of infection at each time) is composed the independent random functions individual, which starts time i...

The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all the research the isolation of infected individuals is disregarded. Hence we focus our study in an epidemic model in a two-layer network, and we use an isola...

sir, the 2014 outbreak of ebola virus disease has beendeclared as an international public health emergencyand since inception, the disease has accounted for almost27,550 cases and 11,235 associated deaths till the endof june 2015 in the affected countries.[1] a wide rangeof factors like lack of preparedness,[2] weak public healthsystem,[3] ineffective diagnostic and case managementservices,[4] ...

We develop a new methodology for the efficient computation of epidemic final size distributions for a broad class of Markovian models. We exploit a particular representation of the stochastic epidemic process to derive a method which is both computationally efficient and numerically stable. The algorithms we present are also physically transparent and so allow us to extend this method from the ...

The Susceptible-Infected-Recovered (SIR) model is studied in multilayer networks with arbitrary number of links across the layers. By following the mapping to bond percolation we give the exact expression for the epidemic threshold and the fraction of the infected individuals in arbitrary number of layers. The case of a multilayer network formed by two interconnected networks is specifically st...