The Dynamic Properties of a Deterministic SIR Epidemic Model in Discrete-Time
نویسندگان
چکیده
منابع مشابه
Behavior of a Discrete SIR Epidemic Model
I. Introduction Infections and infectious diseases are a great burden on many societies, including the countries. An epidemic may be described as a sudden outbreak of a disease that infects a substantial portion of the population in a region before it disappears. In the nineteenth century, recurrent waves of cholera killed millions in India. The influenza epidemic of 1918-1919 killed at least 2...
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Discrete-time models, or difference equations, of some well-known SI, SIR, and SIS epidemic models are considered. The discrete-time SI and SIR models give rise to systems of nonlinear difference equations that are similar in behavior to their continuous analogues under the natural restriction that solutions to the discrete-time models be positive. It is important that the entire system be cons...
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During the course of a day an individual typically mixes with different groups of individuals. Epidemic models incorporating population structure with individuals being able to infect different groups of individuals have received extensive attention in the literature. However, almost exclusively the models assume that individuals are able to simultaneously infect members of all groups, whereas ...
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In this paper, a discrete-time SIR epidemic model with nonlinear incidence rate, time delays and impulses is investigated. Sufficient conditions for the existence and uniqueness of periodic solutions are obtained by using contraction theorem and inequality techniques. An example is employed to illustrate our results. Keywords—Discrete-time SIR epidemic model, Time delay, Nonlinear incidence rat...
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ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2015
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2015.610148