Epidemic SIR Disease Model
Epidemic Propagation: An Automaton Model as the Continuous SIR Model
... infectious disease into a pandemic, perhaps spreading all over the ...an epidemic will start and how it will ...aim. SIR models, introduced for the first time in 1927 by Kermack and Mc Kendrick [1], ...
6
The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm
... of disease has been an indispensable tool in accounting for disease transmission dynamics as well as disease ...Epidemiological disease models have been used to explain the dynamics of ...
6
Global stability of the endemic equilibrium of a discrete SIR epidemic model
... infectious disease and it is spread from person to person by coughing or ...The SIR model is suitable to describe the infection of mumps due to its permanent ...of model parame- ters are ...
19
Dynamics of an SIR epidemic model with stage structure and pulse vaccination
... Pulse vaccination is an important strategy to eradicate an infectious disease. In this paper, we investigate an SIR epidemic model with stage structure and pulse vaccination. By using the ...
17
Stability and Hopf bifurcation analysis of SIR epidemic model with time delay
... is SIR- a concept that elegantly describes a disease that promises immunity against re-infection and indicates that the passage of individuals is from the susceptible class S to the infective class I and ...
5
A stochastic SIR epidemic model with density dependent birth rate
... Stochastic SIR models have been investigated in recent ...stochastic SIR model with or without distributed time delay, they gave a sufficient condition for the asymptotic stability of the ...
12
Optimal Vaccination Strategies of an SIR Epidemic Model with a Saturated Treatment
... nary equation model system with a given constraint. The aim of this work is not to consider a special disease but to set up an optimal control problem relative to the SIR model. To do this, we ...
7
A Stochastic Information Diffusion Model in Social Networks Based on SIR Epidemic Model
... on epidemic diseases. Information dissemination epidemic models have been developed for different network topologies, ...cascade model (ICM)[4] , which is widely adopted in describing the information ...
7
A fractional order SIR epidemic model with nonlinear incidence rate
... In system (1), S(t), I(t), and R(t) represent the numbers of susceptible, infective, and re- covered individuals at time t, respectively. is the recruitment rate of the population, μ is the natural death rate, while d is ...
9
Dynamics of a Nonautonomous SIR Model with Time Varying Impulsive Release and General Nonlinear Incidence Rate in a Polluted Environment
... of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate ...
13
Stability Analysis of an SIR Epidemic Model with Non Linear Incidence Rate and Treatment
... of epidemic disease incorporated a modified SIR epidemic model with generalized incidence ...the disease-free equilibrium and endemic equilibrium with a nonlinear incidence ...pf ...
7
Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent
... delayed SIR epidemic models with a class of nonlinear incidence rates, at the same time, they proved disease-free equilibrium was globally asymptotically stable and endemic equilib- rium was ...
9
Bifurcation and Stability Analysis of a Discrete Time Sir Epidemic Model with Vaccination
... One of the other famous examples identified by these systems are epidemic models [10]. Modeling an outbreak that is progressing through the population allows us to examine the consequences of ways of preventing or ...
12
Asymptotic behavior of a regime switching SIR epidemic model with degenerate diffusion
... cording to Theorem 3.1, the disease is persistent (see Figure 1). In fact, the condition β (i) > α(i)(ε(i) + γ (i)), i ∈ S is not necessary (see Figure 2). In the proof of Theorem 3.1, such a condition is ...
10
Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization
... mathematical model that is quite widely used is the model in the form of differential ...the model of motion, whether it is a spring, pendulum or aircraft maneuver, is expressed in a system of ...
11
The Dynamic Properties of a Deterministic SIR Epidemic Model in Discrete Time
... The organization of this paper is as follows. In next section, we identify all cases of non- and hyperbolic equi- libria, which is a fundament for all succeeding studies. In Section 4, we discuss the transcritical ...
11
An Analysis of a Partial Temporary Immunity SIR Epidemic Model with Nonlinear Treatment Rate
... In this section, the local bifurcation (such as saddle-node , transcritical and pitchfork) is studied to find out the influence of changing one of the parameters value, on the dynamical behavior of system (1) around the ...
9
Existence of a Nonautonomous SIR Epidemic Model with Age Structure
... the disease to become endemic and describing the stability of steady-state solutions, often under the assumption that the population has reached its steady state and the diseases do not affect the death rate of the ...
23
Bifurcations for a deterministic SIR epidemic model in discrete time
... the disease-free equilibrium point and the endemic equilibrium point under certain restrictive conditions of α, β, and γ ...a disease-free equilibrium point and flip bifurcation (or period-doubling ...
16
Global Analysis for a Delay-Distributed SIR Epidemic Model
... Abstract. One of the most tools for describing the incubation period in the epidemiological dynamic models is the distributed delays. In this paper, we propose a delay-distributed SIR epidemic model ...
6