Browsing by Author "Kuldeep Kumar Tripathi"

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Modeling the effects of psychological fear and media-induced awareness on the dynamics of infectious diseases
(American Institute of Mathematical Sciences, 2024) A.K. Misra; Kuldeep Kumar Tripathi; Maitri Verma
The outbreak of an infectious disease in a community creates psychological fear in the population that stimulates the individuals to adopt appropriate behavioral changes to reduce the risk of contracting the infection. The awareness created by mass media is another important factor that motivates people to comply with the precautionary measures required to inhibit the transmission of disease. A study of the combined effects of psychological fear and media-induced awareness on the transmission dynamics of an infectious disease is crucial for designing strategies to control the spread of the infectious disease in a community. This work presents a mathematical model to assess the combined effects of fear and media advertisements on the dynamics of infectious diseases. The stability properties of the solutions of the proposed system are investigated. It is found that if the growth rate of media advertisements exceeds a threshold value, the system enters into limit cycle oscillations from stable equilibrium via Hopf-bifurcation. The amplitude of these periodic oscillations increases with the increase in the growth rate of media advertisements. An increase in the degree of fear in the community may dampen the amplitude of periodic oscillations and above a threshold value of the fear factor, the periodic oscillations die out and endemic equilibrium gets stabilized. It is also found that the high level of fear reduces the effect of the increase in the growth rate of media advertisements and the dissemination rate of awareness among susceptible individuals on the control of infection in the population. © 2024 American Institute of Mathematical Sciences. All rights reserved.
Modeling the effects of psychological fear, media-induced awareness, and sanitation efforts on the dynamics of bacterial diseases
(Springer Science and Business Media Deutschland GmbH, 2025) Kuldeep Kumar Tripathi; Maitri Verma; Arvind Kumar Misra
Bacterial diseases significantly impact human health and the economy, posing serious challenges to societal well-being. Psychological fear of infection motivates behavioral changes to reduce contacts with infected individuals. Awareness campaigns play a crucial role in educating the public about precautionary measures, thereby reducing the likelihood of bacteria ingestion from contaminated sources. Furthermore, individuals who are informed through such campaigns often implement sanitation practices that help to reduce bacterial density in the environment. This study develops a nonlinear mathematical model to analyze the effects of psychological fear, media-induced awareness, and sanitation practices on bacterial disease dynamics. The model considers infection transmission through direct contacts with infected individuals and indirect exposure to environmental bacteria, assuming bacterial density increases proportional to the infected population. Results show that psychological fear, media-driven awareness, and sanitation play crucial roles in shaping bacterial disease dynamics. A higher growth rate of media advertisements induces limit cycle oscillations in the system via Hopf-bifurcation. However, these oscillations diminish when psychological fear surpasses a threshold. Furthermore, it is found that increasing efficacy of media advertisements in promoting precautionary behaviors and enhancing the depletion rate of bacteria through sanitation efforts by aware individuals can reduce disease prevalence. However, these measures may also induce periodic oscillations by lowering the Hopf-bifurcation threshold for media advertisements growth. An increase in the depletion rate of bacteria due to sanitation efforts can also lead to stability switch via double Hopf-bifurcation, underscoring the need for balanced sanitation strategies to prevent oscillations while ensuring effective disease control. © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025.
MODELING THE EFFECTS OF PSYCHOLOGICAL FEAR, TV AND SOCIAL MEDIA ADVERTISEMENTS ON THE CONTROL OF INFECTIOUS DISEASES
(World Scientific, 2025) Maitri Verma; Kuldeep Kumar Tripathi; Arvind Kumar Misra
In this paper, a mathematical model is proposed to study the combined effects of media awareness and fear-induced behavioral changes on the dynamics of infectious diseases. It is considered that in comparison to the unaware individuals, the aware individuals have a lower contact with infected ones. The number of media advertisements is assumed to increase at a rate proportional to the number of infected persons and declines as the number of aware individuals increases. The stability analysis of the model shows that an increase in the growth rate of media advertisements leads to generation of periodic oscillations in the system due to occurrence of Hopf-bifurcation at interior equilibrium. The fear factor and the decline in advertisements due to an increase in the number of aware individuals are found to have stabilizing effect on dynamics of system and their high values can eliminate the limit cycle oscillations present in the system. The rate at which awareness spreads among susceptible individuals and the behavioral response of the aware population are found to be the critical parameters which shape the overall impact of awareness on disease dynamics. It has been observed that the increase in contact rate of aware individuals with infected ones and the dissemination rate of awareness can result into emergence of multiple stability switches via double Hopf-bifurcation. © 2025 World Scientific Publishing Company.