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

Arvind Kumar Misra; Rajanish Kumar Rai; Yasuhiro Takeuchi; Arvind Kumar Misra; Rajanish Kumar Rai; Yasuhiro Takeuchi

doi:10.3934/mbe.2018061

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 6: 1315-1343. doi: 10.3934/mbe.2018061

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

1.
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221005, India
2.
College of Science and Engineering, Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan

Received: 26 September 2017 Revised: 25 April 2018 Published: 01 December 2018
MSC : Primary: 34A34, 34D20, 92D30

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.
- TV advertisements,
- social media,
- awareness,
- stability,
- Hopf-bifurcation,
- stability switch
Citation: Arvind Kumar Misra, Rajanish Kumar Rai, Yasuhiro Takeuchi. Modeling the control of infectious diseases: Effects of TV and social media advertisements[J]. Mathematical Biosciences and Engineering, 2018, 15(6): 1315-1343. doi: 10.3934/mbe.2018061

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Abstract

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.

References

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