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A dynamic model for infectious diseases: The role of vaccination and treatment

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  • Raja Sekhara Rao, P.
  • Naresh Kumar, M.

Abstract

Understanding dynamics of an infectious disease helps in designing appropriate strategies for containing its spread in a population. Recent mathematical models are aimed at studying dynamics of some specific types of infectious diseases. In this paper we propose a new model for infectious diseases spread having susceptible, infected, and recovered populations and study its dynamics in presence of incubation delays and relapse of the disease. The influence of treatment and vaccination efforts on the spread of infection in presence of time delays are studied. Sufficient conditions for local stability of the equilibria and change of stability are derived in various cases. The problem of global stability is studied for an important special case of the model. Simulations carried out in this study brought out the importance of treatment rate in controlling the disease spread. It is observed that incubation delays have influence on the system even under enhanced vaccination. The present study has clearly brought out the fact that treatment rate even in presence of time delays would contain the disease as compared to popular belief that eradication can only be done through vaccination.

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  • Raja Sekhara Rao, P. & Naresh Kumar, M., 2015. "A dynamic model for infectious diseases: The role of vaccination and treatment," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 34-49.
    • Handle: RePEc:eee:chsofr:v:75:y:2015:i:c:p:34-49
    DOI: 10.1016/j.chaos.2015.02.004
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    Cited by:

    1. Ding, Chunxiao & Tao, Nana & Sun, Yun & Zhu, Yuanguo, 2016. "The effect of time delays on transmission dynamics of schistosomiasis," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 360-371.
    2. Anand, Monalisa & Danumjaya, P. & Rao, P. Raja Sekhara, 2023. "A nonlinear mathematical model on the Covid-19 transmission pattern among diabetic and non-diabetic population," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 346-369.
    3. Fatima, Bibi & Zaman, Gul, 2020. "Co-infection of Middle Eastern respiratory syndrome coronavirus and pulmonary tuberculosis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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