Role of media and treatment on an SIR model

Dubey, B.; Dubey, Preeti; Dubey, Uma S.

doi:10.15388/na.2016.2.3

Cited by 41 publications

(20 citation statements)

References 18 publications

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“…These programs induce behavioral changes in the population, which divide the susceptible class into 2 subclasses, ie, aware susceptible and unaware susceptible, and their study reveals that awareness programs play a crucial role in controlling the disease during an epidemic outbreak. However, awareness programs alone cannot eradicate the disease outbreak, treatment of the disease in infected population must go along with awareness programs for the susceptible …”

Section: Introductionmentioning

confidence: 99%

“…However, awareness programs alone cannot eradicate the disease outbreak, treatment of the disease in infected population must go along with awareness programs for the susceptible. 12 The Pontryagin's maximum principle in optimal control theory introduced by Pontryagin et al 13 and later developed by Fleming and Rishel 14 is successfully applied in a number of studies to explore optimal control theory in some mathematical models for infectious diseases including HIV diseases, [15][16][17][18][19] pandemic influenza, and vectorborne diseases. 20 Okosun et al 18 investigated the fundamental role of optimal control theory to explore the impact of treatment and screening of unaware infectives on HIV/AIDS epidemic.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control for the spread of infectious disease: The role of awareness programs by media and antiviral treatment

Gani

2018

Optim Control Appl Methods

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Summary This paper presents a detailed mathematical analysis of the role of awareness programs by media and antiviral treatment on the control of infectious diseases. A nonlinear model is proposed in order to control the infectious diseases, and the model is examined under various scenarios of control measures using variety of mathematical techniques including stability, sensitivity, optimal control, and cost‐effectiveness analysis. Considering the constant control parameters, the basic reproduction number is derived and investigated by the existence and stability of equilibria, then the relative impact of each of the constant control parameters are assessed by calculating the sensitivity index of the basic reproduction number. Under the time‐dependent controls, the necessary conditions for the optimal control of the disease are derived using the Pontryagin's maximum principle in order to determine optimal strategies for controlling the spread of the disease. In order to investigate the most cost‐effective control strategy among all the possible strategies, cost‐effectiveness analysis is carried out using numerical simulations and the result reveals that the strategy combination of 3 control measures (the successful campaign of awareness programs by media, controlling effort that alters infectious cases receiving treatment, and strengthening effort made on awareness campaign programs) is the most cost‐effective control strategy and this indicates that implementation of all the 3 control measures is necessary in order to control the disease outbreak.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal control for the spread of infectious disease: The role of awareness programs by media and antiviral treatment

Gani

2018

Optim Control Appl Methods

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“…Over the past few decades, several mathematical studies have been done to assess the effects of media campaigns for the control of infectious diseases . In previous studies, it is assumed that the number of awareness programs is implemented proportional to the number of infected individuals by considering media as a dynamic variable or transmission rate as decreasing function of number of infected individuals due to media alerts.…”

Section: Introductionmentioning

confidence: 99%

“…Over the past few decades, several mathematical studies have been done to assess the effects of media campaigns for the control of infectious diseases. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] In previous studies, it is assumed that the number of awareness programs is implemented proportional to the number of infected individuals by considering media as a dynamic variable or transmission rate as decreasing function of number of infected individuals due to media alerts. In particular, Misra et al 17 have studied an SIS model to see the impact of media campaigns on the prevalence of an infectious disease by considering the media campaigns as a dynamic variable.…”

Section: Introductionmentioning

confidence: 99%

Impacts of TV and radio advertisements on the dynamics of an infectious disease: A modeling study

Misra

Kumar

2018

Math Methods in App Sciences

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TV and radio advertisements are widely acknowledged as important interventions in raising issues of public health care and play promising role to control the infection through propagating awareness among the individuals. In this paper, a nonlinear susceptible‐infected‐susceptible (SIS) model is proposed and analyzed to see the impacts of TV and radio advertisements on the spread of influenza epidemic. In the model formulation, it is assumed that the susceptible individuals contract infection through the direct contact with infected individuals. The information regarding the protection against the disease is propagated via TV and radio advertisements, and their growth rates are assumed to be proportional to the fraction of infected individuals. However, the growth rate of TV advertisements decreases with the increase in number of aware individuals. The information broadcasted through TV and radio advertisements induces behavioral changes among the susceptible individuals, and they form an isolated aware class. The epidemiological feasible equilibria, their stability properties, and direction of bifurcation are discussed. The expression for modified basic reproduction number is obtained. The model analysis shows that the dissemination rate of awareness among susceptible individuals due to TV and radio advertisements and baseline number of TV and radio advertisements have potential to reduce the epidemic peak and, thus, control the spread of infection. Further, the analytical findings are well supported through numerical simulation.

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“…In the recent past, some studies have been conducted to assess the impact of media to control the spread of infectious diseases [11,13,27,28,29,41,37,38,36,43,44]. In particular, Sun et al [41] have studied an SIS model to see the effect of media-induced social distancing on disease prevalence in two patch.…”

mentioning

confidence: 99%

Modeling the control of infectious diseases: Effects of TV and social media advertisements

Misra

Kumar²,

Takeuchi

2018

Mathematical Biosciences &Amp; Engineering

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Public health information through media plays an important role to curb the spread of various infectious diseases as most of the populations rely on what media projects to them. Social media and TV advertisements are important mediums to communicate people regarding the spread of any infectious disease and methods to prevent its spread. Therefore, in this paper, we propose a mathematical model to see how TV and social media advertisements impact the dynamics of an infectious disease. The susceptible population is assumed vulnerable to infection as well as information (through TV and social media ads). It is also assumed that the growth rate of TV and social media ads is proportional to the number of infected individuals with decreasing function of aware individuals. The feasibility of possible equilibria and their stability properties are discussed. It is shown that the increment in growth rate of TV and social media ads destabilizes the system and periodic oscillations arise through Hopf-bifurcation. It is also found that the increase in dissemination rate of awareness among susceptible population also gives rise interesting dynamics about the stability of endemic equilibrium and causes stability switch. It is observed that TV and social media advertisements regarding the spread of infectious diseases have the potential to bring behavioral changes among the people and control the spread of diseases. Numerical simulations also support analytical findings.

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Role of media and treatment on an SIR model

Cited by 41 publications

References 18 publications

Optimal control for the spread of infectious disease: The role of awareness programs by media and antiviral treatment

Optimal control for the spread of infectious disease: The role of awareness programs by media and antiviral treatment

Impacts of TV and radio advertisements on the dynamics of an infectious disease: A modeling study

Modeling the control of infectious diseases: Effects of TV and social media advertisements

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