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Nonlinear dynamics of infectious diseases via information-induced vaccination and saturated treatment

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  • Kumar, Anuj
  • Srivastava, Prashant K.
  • Gupta, R.P.

Abstract

The present study of a nonlinear compartmental SVIR model accounts for the dynamics of infectious diseases in population. In this model, the effect of information on vaccination coverage is quantified when medical resources are limited during the epidemic outbreak. Model analysis is performed and the global asymptotic stability of the disease free equilibrium is established when treatment is available for all infective individuals. However, the existence of multiple endemic equilibria is observed due to saturation in medical treatment and information-induced vaccination coverage. If the basic reproduction number is greater than unity, a unique endemic equilibrium for the model is obtained under some parametric conditions. Using the geometric approach, the global asymptotic stability of this endemic equilibrium is established under a parametric constraint. Further, when medical resources are limited, the existence Hopf bifurcation is shown analytically, which infers the oscillatory persistence of disease within the population. Occurrence of Hopf–Hopf bifurcation is also investigated numerically. At first Hopf bifurcation threshold, an endemic equilibrium loses its stability and produces oscillations, and further, it regains its stability at another Hopf bifurcation threshold when oscillations disappear. Hence, multiple stability switches are observed due to the saturated treatment and information-induced vaccination. The effect of the fading of memory also plays a crucial role and gives rise to complex dynamical behaviour and also affects the stability properties. Numerically, different types of backward bifurcation are also examined. Extensive numerical experimentations are also carried out to further explore the model system.

Suggested Citation

  • Kumar, Anuj & Srivastava, Prashant K. & Gupta, R.P., 2019. "Nonlinear dynamics of infectious diseases via information-induced vaccination and saturated treatment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 77-99.
    • Handle: RePEc:eee:matcom:v:157:y:2019:i:c:p:77-99
    DOI: 10.1016/j.matcom.2018.09.024
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    References listed on IDEAS

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    1. Zhou, Yugui & Xiao, Dongmei & Li, Yilong, 2007. "Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1903-1915.
    2. Tomas Philipson, 1996. "Private Vaccination and Public Health: An Empirical Examination for U.S. Measles," Journal of Human Resources, University of Wisconsin Press, vol. 31(3), pages 611-630.
    3. Avner Ahituv & V. Joseph Hotz & Tomas Philipson, 1996. "The Responsiveness of the Demand for Condoms to the Local Prevalence of AIDS," Journal of Human Resources, University of Wisconsin Press, vol. 31(4), pages 869-897.
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    Cited by:

    1. Gupta, R.P. & Kumar, Arun, 2022. "Endemic bubble and multiple cusps generated by saturated treatment of an SIR model through Hopf and Bogdanov–Takens bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 1-21.
    2. Kumar, Anuj & Srivastava, Prashant K. & Dong, Yueping & Takeuchi, Yasuhiro, 2020. "Optimal control of infectious disease: Information-induced vaccination and limited treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    3. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. Pan Tang & Shiwen Qian & Lei Shi & Longxing Qi & Tingting Li, 2023. "The Influence of Migration to Regions with Different Coverages of Health Education on Schistosomiasis," Mathematics, MDPI, vol. 11(12), pages 1-27, June.

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