Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate

Sahu, Govind Prasad; Dhar, Joydip

doi:10.1016/j.apm.2011.07.044

Cited by 75 publications

(66 citation statements)

References 34 publications

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“…This individu will stay in the exposed class during the exposed period. After the exposed period end or the immune decrease, the individu is in the class of infection and shows symptoms and then transmit the disease [8].…”

Section: Issn 2087-2852 E-issn 2338-1655mentioning

confidence: 99%

Optimal Control on Model of SARS Disease Spread with Vaccination and Treatment

Sari

Habibah

Widodo

2017

JELS

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The spread of SARS (Severe Acute Respiratory Syndrome) disease in a human population is one of the phenomena that can be mathematically modeled. The exposed period of SARS disease underlies the formation of the SVEIR epidemic model which is a modification of the SVIR epidemic model by adding subpopulation E (exposed). In the SVEIR model, there are two control variables in the form of vaccination and treatment which aimed to minimize exposed subpopulation, infected subpopulation, and control implementation cost. The Pontryagin's minimum principle is used to obtain optimal control and system, thus minimizing objective functional as the objective to be achieved. Furthermore, the forward-backward sweep method is used for numerical simulation in order to determine the most appropriate control strategy in a finite time. The simulation results show that implementation of both vaccination and treatment is the most effective decision making to control the spread of SARS disease.

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Section: Issn 2087-2852 E-issn 2338-1655mentioning

confidence: 99%

Optimal Control on Model of SARS Disease Spread with Vaccination and Treatment

Sari

Habibah

Widodo

2017

JELS

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“…Consider the autonomous dynamical system Lemma 4.1. [19]. Suppose that assumptions ðH 1 Þ and ðH 2 Þ hold.…”

Section: Global Stabilities Of the Equilibriamentioning

confidence: 99%

A mathematical model approach for tobacco control in China

Pang

Zhao

Liu

et al. 2015

Applied Mathematics and Computation

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“…It follows that for the proposed compartmental model, local stability of adopter free equilibrium is governed by the basic influence number of model.The basic influence number R 0 , is defined as the expected number of secondary adoption caused by an adopter individual upon entering a totally non-adopter population, as similar to the disease spreading models [22]. Using the notation in [22,23], we have two vectors F and V to represent the new infection term and remaining transfer terms, respectively:…”

Section: Steady State Basic Influence Number and Stabilitymentioning

confidence: 99%

The impact of media on a new product innovation diffusion: a mathematical model

Dhar¹,

Tyagi²,

Sinha³

2014

B Soc Paran Mat

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In this paper, we proposed a three compartment model consisting of non-adopter, adopter and frustrated classes of population to discuss the influence of media coverage in spreading and controlling of adopter of a particular product in a region. The model exhibits two equilibria:(i) a adopter-free and (ii) unique interior equilibrium. Stability analysis of the model shows that the adopter-free equilibrium is always locally asymptotically stable if the influence number of adopter (R 0 ), which depends on parameters of the system is less than unity. Otherwise if R 0 > 1, a unique interior equilibrium exists, it is locally asymptotically stable under some set of conditions. Further analytically and numerically it is observed that the region for backward bifurcation of adopter population increases with the decrease of the valid contact rate before media alert. Finally, numerically experimentation are presented to establish the effect of different media alert rate on adopter and non adopter population.

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Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate

Cited by 75 publications

References 34 publications

Optimal Control on Model of SARS Disease Spread with Vaccination and Treatment

Optimal Control on Model of SARS Disease Spread with Vaccination and Treatment

A mathematical model approach for tobacco control in China

The impact of media on a new product innovation diffusion: a mathematical model

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