The deterministic SIR model for disease spread in a closed population is extended to allow infected individuals to recover to the susceptible state. This extension preserves the second constant of motion, i.e., a functional relationship of susceptibl...
This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing i...
The SIR model of epidemic spreading can be reduced to a nonlinear differential equation with an exponential nonlinearity. This differential equation can be approximated by a sequence of nonlinear differential equations with polynomial nonlinearities....
In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using...
This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors,...
So called SIR epidemic model with distributed delay and stochastic perturbations is considered. It is shown, that the known sufficient conditions of stability in probability of the equilibria of this model, formulated immediately in the terms of the...
In this article, we study the fractional SIR epidemic model with the Atangana–Baleanu–Caputo fractional operator. We explore the properties and applicability of the ZZ transformation on the Atangana–Baleanu–Caputo fractional o...
With outbreaks of epidemics, an enormous loss of life and property has been caused. Based on the influence of disease transmission and information propagation on the transmission characteristics of infectious diseases, in this paper, a fractional-ord...
In this paper, we are concerned with the asymptotic stability of the nontrivial endemic equilibrium of an age-structured susceptible-infective-recovered (SIR) epidemic model. For a special form of the disease transmission function, we perform the red...
In this paper, a numerical study has been undertaken on the susceptible-infected-recovered (SIR) epidemic model that encompasses the mechanisms of the evolution of disease transmission; a prophylactic vaccination strategy in the susceptible populatio...
Drilling activity produces a significant amount of road traffic through unpaved and paved local roads. Because oil production is an important contributor to the local economy in the state of North Dakota, the state and local transportation agencies m...
Risk propagation is occurring as an exceptional challenge to supply chain management. Identifying which supplier has the greater possibility of interruptions is pivotal for managing the occurrence of these risks, which have a significant impact on th...
A SIR epidemic model that describes the dynamics of childhood disease with a saturated incidence rate and vaccination program at a constant rate was investigated. For the continuous model we first show its basic properties, namely, the non-negativity...
Monitored differential infection rates of past corona waves are used to infer, a posteriori, the real time variation of the ratio of recovery to infection rate as a key parameter of the SIR (susceptible-infected-recovered/removed) epidemic model. Fro...
28 January 2022
This paper presents and studies a new epidemic SIR (Susceptible–Infectious–Recovered) model with susceptible recruitment and eventual joint vaccination efforts for both newborn and susceptible individuals. Furthermore, saturation effects...
Analytically and numerically, the study examines the stability and local bifurcations of a discrete-time SIR epidemic model. For this model, a number of bifurcations are studied, including the transcritical, flip bifurcations, Neimark–Sacker bi...
This article proposes a stochastic SIR model with general nonlinear incidence and Lévy jumps, which is used to describe diseases spreading in human populations. The model takes into account the randomness and sublinearity of diseases and can m...
Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical epidemiology has one basic general law, the “R0 alternative&rdqu...
The paper mainly investigates a stochastic SIRS epidemic model with Logistic birth and nonlinear incidence. We obtain a new threshold value (R0m) through the Stratonovich stochastic differential equation, different from the usual basic reproduction n...
Two non-standard predictor-corrector type finite difference methods for a SIR epidemic model are proposed. The methods have useful and significant features, such as positivity, basic stability, boundedness and preservation of the conservation laws. T...
In the past decade years, much attention has been attached on assembly process reliability in manufacturing system, because the quality and cost of product are highly determined by assembly process. However, existing research on reliability in assemb...
This paper aims to present two nonstandard finite difference (NFSD) methods to solve an SIR epidemic model. The proposed methods have important properties such as positivity and boundedness and they also preserve conservation law. Numerical compariso...
The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the mathematical community to derive an explicit solution. The present paper reports novel analytical results...
This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). The SIR epidemic model is proposed and solved under different un...
A simple model for predicting Coronavirus Disease 2019 (COVID-19) epidemic is presented in this study. The prediction model is presented based on the classic Susceptible-Infectious-Recovered (SIR) model, which has been widely used to describe the epi...
In this paper, a new numerical scheme, which we call the impulsive linearly implicit Euler method, for the SIR epidemic model with pulse vaccination strategy is constructed based on the linearly implicit Euler method. The sufficient conditions for gl...
Susceptible-infectious-removed (SIR) epidemic models are proposed to consider the impact of available resources of the public health care system in terms of the number of hospital beds. Both the incidence rate and the recovery rate are considered as...
Mathematical models of the spread of epidemic diseases are studied, paying special attention to networks. We treat the Susceptible-Infected-Recovered (SIR) model and the Susceptible-Exposed-Infectious-Recovered (SEIR) model described by differential...
This paper is concerned with the asymptotical behavior of the impulsive linearly implicit Euler method for the SIR epidemic model with nonlinear incidence rates and proportional impulsive vaccination. We point out the solution of the impulsive linear...
Different strains of influenza viruses spread in human populations during every epidemic season. As the size of an infected population increases, the virus can mutate itself and grow in strength. The traditional epidemic SIR model does not capture vi...
11 July 2019
We present a series of SIR-network models, extended with a game-theoretic treatment of imitation dynamics which result from regular population mobility across residential and work areas and the ensuing interactions. Each considered SIR-network model...
The outbreaks of large-scale epidemics, such as COVID-19 in 2019–2022, challenge modelers. Beside the effect of the incubation period of the virus, the delay property of detection should be also stressed. This kind of memory effect affects the...
The integrable versions of SIR epidemic models are introduced. The exact solutions of these models are derived. The advantage of these models is the possibility of full analysis of obtained solutions and the simplicity of explicit formulas for the im...
At the end of 2019, an outbreak of the novel coronavirus (COVID-19) made a profound impact on the country’s production and people’s daily lives. Up until now, COVID-19 has not been fully controlled all over the world. Based on the clinical research p...
We investigate how homophily in adherence to anti-epidemic measures affects the final size of epidemics in social networks. Using a modified SIR model, we divide agents into two behavioral groups—compliant and non-compliant—and introduce...
This paper introduces the mathematical formalization of two probabilistic procedures for susceptible-infected-recovered (SIR) and susceptible-infected-susceptible (SIS) infectious diseases epidemic models, over Erdös-Rényi contact network...
Infectious-disease dynamics depend on heterogeneous contact structure, which classical homogeneous-mixing models such as SIR/SEIR cannot capture. We develop a curvature-informed network SIR framework that embeds Forman–Ricci curvature (FRC), a...
Revisiting the classical model by Ross and Kermack-McKendrick, the Susceptible–Infectious–Recovered (SIR) model used to formalize the COVID-19 epidemic, requires improvements which will be the subject of this article. The heterogeneity in...
The results presented in this paper deal with the existence of solutions of a first order fully coupled system of three equations, and they are split in two parts: 1. Case with coupled functional boundary conditions, and 2. Case with periodic boundar...
We propose a real-time approximation of R0 in an SIR-type model that applies to the COVID-19 epidemic outbreak. A very useful direct formula expressing R0 is found. Then, various type of models are considered, namely, finite differences, cubic spline...
21 December 2020
As of November 2020, the number of COVID-19 cases was increasing rapidly in many countries. In Europe, the virus spread slowed considerably in the late spring due to strict lockdown, but a second wave of the pandemic grew throughout the fall. In this...
In order to investigate the impact of two immunization strategies—vaccination targeting susceptible individuals to reduce their infection rate and clinical medical interventions targeting infected individuals to enhance their recovery rate&mdas...
Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call respectively “suscept...
We discuss the spread of a piece of news in a population. This is modeled by SIR model of epidemic spread. The model can be reduced to a nonlinear differential equation for the number of people affected by the news of interest. The differential equat...
Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology...
The susceptible–infected–recovered–vaccinated–deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encomp...
This study investigates the dynamic behavior of an SIRS epidemic model in discrete time, focusing primarily on mathematical analysis. We identify two equilibrium points, disease-free and endemic, with our main focus on the stability of the endemic st...
Stochastic SIRS models play a key role in formulating and analyzing the transmission of infectious diseases. These models reflect the environmental changes of the diseases and their biological mechanisms. Therefore, it is very important to study the...
The recent outbreak of COVID-19 underlined the need for a fast and trustworthy methodology to identify the features of a pandemic, whose early identification is of help for designing non-pharmaceutical interventions (including lockdown and social dis...
In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medi...
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