Journal ArticleDOI
The explicit series solution of SIR and SIS epidemic models
TLDR
The SIR and SIS epidemic models in biology are solved by means of an analytic technique for nonlinear problems, namely the homotopy analysis method (HAM), and a one-parameter family of explicit series solutions are obtained.About:
This article is published in Applied Mathematics and Computation.The article was published on 2009-09-01. It has received 97 citations till now. The article focuses on the topics: Homotopy analysis method & Convergent series.read more
Citations
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On a Generalized Time-Varying SEIR Epidemic Model with Mixed Point and Distributed Time-Varying Delays and Combined Regular and Impulsive Vaccination Controls
TL;DR: In this article, a generalized time-varying SEIR propagation disease model subject to delays is discussed, which potentially involves mixed regular and impulsive vaccination rules, and the proposed regular vaccination control objective is the tracking of a prescribed suited infectious trajectory for a set of given initial conditions.
Journal ArticleDOI
Accurate closed-form solution of the SIR epidemic model.
TL;DR: An accurate closed-form solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et al., 2017).
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On the Existence of Equilibrium Points, Boundedness, Oscillating Behavior and Positivity of a SVEIRS Epidemic Model under Constant and Impulsive Vaccination
TL;DR: In this article, the disease-free and endemic equilibrium points of a SVEIRS propagation disease model with a regular constant vaccination were discussed and the positivity of such a model was also discussed as well as the boundedness of the total and partial populations.
Journal ArticleDOI
Investigation of epidemic spreading process on multiplex networks by incorporating fatal properties.
TL;DR: A two-layered multiplex network model (usually composed of a virtual layer sustaining unaware-aware-unaware (UAU) dynamics and a physical one supporting susceptible-infected-recovered-dead (SIRD) process) is presented to investigate the spreading property of fatal epidemics in this manuscript.
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Vaccination strategies based on feedback control techniques for a general SEIR-epidemic model
TL;DR: Several simple linear vaccination-based control strategies for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model for vaccination control of susceptible and infected populations are presented.
References
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Journal ArticleDOI
A contribution to the mathematical theory of epidemics
TL;DR: In this article, the authors considered the problem of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population.
A Contribution to the Mathematical Theory of Epidemics.
TL;DR: The present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.
Journal ArticleDOI
The Mathematics of Infectious Diseases
TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
Journal ArticleDOI
On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations
TL;DR: It is shown that in certain special cases one can easily compute or estimate the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population.
On the definition and the computation of the basic reproduction ratio : $R_ 0$ in models for infectious diseases in heterogeneous populations
TL;DR: In this paper, the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is defined as the dominant eigenvalue of a positive linear operator.
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