Stochastic Analysis of an Influenza Epidemic Model

Muhammad Waleed; Mudassar Imran; Adnan Khan

doi:10.1007/s40819-015-0118-7

Stochastic Analysis of an Influenza Epidemic Model

Muhammad Waleed
, Mudassar Imran
, Adnan Khan

University of Maine
Gulf University for Science and Technology
Lahore University of Management Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper, a deterministic model for the transmission dynamics of influenza is formulated which, in particular, takes into account the effects of medication as well as hospitalization. We present results related to the existence of disease-free or endemic equilibrium. We also perform uncertainty and sensitivity analysis of the basic reproduction number R _o . The main purpose of this paper, however, is to formulate a stochastic analogue of the deterministic model, and perform its analysis with the help of numerical simulations to get insights about the infection in a stochastic environment and compare its dynamics with the deterministic case.

Original language	English
Pages (from-to)	425-443
Number of pages	19
Journal	International Journal of Applied and Computational Mathematics
Volume	3
Issue number	2
DOIs	https://doi.org/10.1007/s40819-015-0118-7
State	Published - 1 Jun 2017
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Basic reproduction number
Continuous time Markov chain (CTMC)
Influenza
Stability analysis
Stochastic analysis

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10.1007/s40819-015-0118-7

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title = "Stochastic Analysis of an Influenza Epidemic Model",

abstract = " In this paper, a deterministic model for the transmission dynamics of influenza is formulated which, in particular, takes into account the effects of medication as well as hospitalization. We present results related to the existence of disease-free or endemic equilibrium. We also perform uncertainty and sensitivity analysis of the basic reproduction number R o . The main purpose of this paper, however, is to formulate a stochastic analogue of the deterministic model, and perform its analysis with the help of numerical simulations to get insights about the infection in a stochastic environment and compare its dynamics with the deterministic case.",

keywords = "Basic reproduction number, Continuous time Markov chain (CTMC), Influenza, Stability analysis, Stochastic analysis",

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T1 - Stochastic Analysis of an Influenza Epidemic Model

AU - Waleed, Muhammad

AU - Imran, Mudassar

AU - Khan, Adnan

PY - 2017/6/1

Y1 - 2017/6/1

N2 - In this paper, a deterministic model for the transmission dynamics of influenza is formulated which, in particular, takes into account the effects of medication as well as hospitalization. We present results related to the existence of disease-free or endemic equilibrium. We also perform uncertainty and sensitivity analysis of the basic reproduction number R o . The main purpose of this paper, however, is to formulate a stochastic analogue of the deterministic model, and perform its analysis with the help of numerical simulations to get insights about the infection in a stochastic environment and compare its dynamics with the deterministic case.

AB - In this paper, a deterministic model for the transmission dynamics of influenza is formulated which, in particular, takes into account the effects of medication as well as hospitalization. We present results related to the existence of disease-free or endemic equilibrium. We also perform uncertainty and sensitivity analysis of the basic reproduction number R o . The main purpose of this paper, however, is to formulate a stochastic analogue of the deterministic model, and perform its analysis with the help of numerical simulations to get insights about the infection in a stochastic environment and compare its dynamics with the deterministic case.

KW - Basic reproduction number

KW - Continuous time Markov chain (CTMC)

KW - Influenza

KW - Stability analysis

KW - Stochastic analysis

UR - https://www.scopus.com/pages/publications/85056099306

U2 - 10.1007/s40819-015-0118-7

DO - 10.1007/s40819-015-0118-7

M3 - Article

AN - SCOPUS:85056099306

SN - 2349-5103

VL - 3

SP - 425

EP - 443

JO - International Journal of Applied and Computational Mathematics

JF - International Journal of Applied and Computational Mathematics

IS - 2

ER -

Stochastic Analysis of an Influenza Epidemic Model

Abstract

UN SDGs

Keywords

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