Hopf bifurcation and stability switches in an infectious disease model with incubation delay, information, and saturated treatment

Das, Tanuja; Srivastava, Prashant K.

doi:10.1007/s12190-022-01702-5

J. Appl. Math. Comput.

2022

DOI: 10.1007/s12190-022-01702-5

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Hopf bifurcation and stability switches in an infectious disease model with incubation delay, information, and saturated treatment

Tanuja Das

Prashant K. Srivastava

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Cited by 3 publications

References 36 publications

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An Integrated Framework for Infectious Disease Control Using Mathematical Modeling and Deep Learning

Salman,

Das,

Mohanty

2025

IEEE Open J. Eng. Med. Biol.

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Infectious diseases are a major global public health concern. Precise modeling and prediction methods are essential to develop effective strategies for disease control. However, data imbalance and the presence of noise and intensity inhomogeneity make disease detection more challenging. Goal: In this article, a novel infectious disease pattern prediction system is proposed by integrating deterministic and stochastic model benefits with the benefits of the deep learning model. Results: The combined benefits yield improvement in the performance of solution prediction. Moreover, the objective is also to investigate the influence of time delay on infection rates and rates associated with vaccination. Conclusions: In this proposed framework, at first, the global stability at disease free equilibrium is effectively analysed using Routh-Haurwitz criteria and Lyapunov method, and the endemic equilibrium is analysed using non-linear Volterra integral equations in the infectious disease model. Unlike the existing model, emphasis is given to suggesting a model that is capable of investigating stability while considering the effect of vaccination and migration rate. Next, the influence of vaccination on the rate of infection is effectively predicted using an efficient deep learning model by employing the long-term dependencies in sequential data. Thus making the prediction more accurate.

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An Integrated Framework for Infectious Disease Control Using Mathematical Modeling and Deep Learning

Salman,

Das,

Mohanty

2025

IEEE Open J. Eng. Med. Biol.

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Stability and Hopf Bifurcation Analysis of a Multi-Delay Vector-Borne Disease Model with Presence Awareness and Media Effect

Hu,

Nie

2023

Fractal Fract

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Vector-borne diseases, being one of the most difficult infectious diseases to understand, model, and control, account for a large proportion of human infectious diseases. In the current transmission process of infectious diseases, the latent period of pathogens in vivo, the influence of media coverage, and the presence of awareness on the spread and control of diseases are important factors that cannot be ignored. Based on this, a novel vector-borne disease model with latent delay and media coverage delay is proposed to discuss the impact of these factors. First, the global existence and ultimate boundedness of solutions for this model are obtained. Further, the exact expressions for the basic reproduction number are given, from which the existence and local stability of the disease-free and endemic equilibria are analyzed. Moreover, using the delay as a bifurcation parameter, we also discuss the existence, direction, and stability of the Hopf bifurcation. Finally, some numerical examples are carried out to explain the main theoretical results and discuss the impacts of the main parameters of this model on the transmission of vector-borne disease.

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Modeling the effects of psychological fear and media-induced awareness on the dynamics of infectious diseases

Misra¹,

Tripathi²,

Verma³

2024

DCDS-B

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Hopf bifurcation and stability switches in an infectious disease model with incubation delay, information, and saturated treatment

Cited by 3 publications

References 36 publications

An Integrated Framework for Infectious Disease Control Using Mathematical Modeling and Deep Learning

An Integrated Framework for Infectious Disease Control Using Mathematical Modeling and Deep Learning

Stability and Hopf Bifurcation Analysis of a Multi-Delay Vector-Borne Disease Model with Presence Awareness and Media Effect

Modeling the effects of psychological fear and media-induced awareness on the dynamics of infectious diseases

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