The explicit series solution of SIR and SIS epidemic models

@article{Khan2009TheES,
  title={The explicit series solution of SIR and SIS epidemic models},
  author={Hina Khan and Ram N. Mohapatra and K. Vajravelu and Shijun Liao},
  journal={Appl. Math. Comput.},
  year={2009},
  volume={215},
  pages={653-669}
}
A note on Exact solution of SIR and SIS epidemic models
In this article we have successfully obtained an exact solution of a particular case of SIR and SIS epidemic models given by Kermack and Mckendrick [1] for constant population, which are described by
Differential Transformation Method (DTM) for Solving SIS and SI Epidemic Models
In this paper, the differential transformation method (DTM) is employed to find the semi-analytical solutions of SIS and SI epidemic models for constant population. Firstly, the theoretical
Numerical Solution of an Interval-Based Uncertain SIR (Susceptible-Infected-Recovered) Epidemic Model by Homotopy Analysis Method
TLDR
The SIR epidemic model is proposed and solved under different uncertain intervals by the HAM to obtain the numerical solution of the model and the results of the stochastic and deterministic models were compared using numerical simulations.
Solution of Fractional SIR Epidemic Model Using Residual Power Series Method
The SIR model with unknown parameters is an important issue for scientists in the study of epidemiology and medical care for the injured people. In this work, an efficient technique based on the
Qualitative and Bifurcation Analysis of an SIR Epidemic Model with Saturated Treatment Function and Nonlinear Pulse Vaccination
An SIR epidemic model with saturated treatment function and nonlinear pulse vaccination is studied. The existence and stability of the disease-free periodic solution are investigated. The sufficient
Stability of SIR Epidemic Model Equilibrium Points
Chapter 11 deals with a mathematical model of the spread of infectious diseases, so called SIR epidemic model. Sufficient conditions for stability in probability of the degenerated equilibrium point
A Method of Directly Defining the inverse Mapping (MDDiM) for solutions of non-linear coupled systems arising in SIR and SIS epidemic models
In this paper, we extend Liao’s newly invented MDDiM for a differential equation to a coupled system of nonlinear differential equations arising in SIR and SIS epidemic models. The method is novel,
On New High Order Iterative Schemes for Solving Initial Value Problems in Epidemiology
Most problems arising from mathematical epidemiology are often described in terms of differential equations. However, it is often very difficult to obtain closed form solutions of such equations,
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 31 REFERENCES
Lyapunov Functions and Global Stability for SIR and SIRS Epidemiological Models with Non-Linear Transmission
TLDR
It is proved that, under the constant population size assumption, the concavity of the function f(S,I) with respect to the number of the infective hosts I ensures the uniqueness and the global stability of the positive endemic equilibrium state.
Models for the simple epidemic.
On the homotopy analysis method for nonlinear problems
  • S. Liao
  • Mathematics, Engineering
    Appl. Math. Comput.
  • 2004
A General Approach to Obtain Series Solutions of Nonlinear Differential Equations
Based on homotopy, which is a basic concept in topology, a general analytic method (namely the homotopy analysis method) is proposed to obtain series solutions of nonlinear differential equations.
The Mathematics of Infectious Diseases
TLDR
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.
...
1
2
3
4
...