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The effect of vaccination on COVID-19 transmission dynamics with comorbidity using reaction–diffusion model

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Abstract

The global emergence of COVID-19 and its widespread transmission posed a formidable challenge for the global medical community. While vaccinations succeeded in mitigating the severity and fatality of the infection, a new challenge emerged: addressing transmission in the presence of comorbidities. A comprehensive mathematical model has been developed to address this issue, incorporating elements such as nonpharmaceutical interventions, vaccination strategies, comorbidity factors, limited healthcare resources, and the impact of nosocomial transmission. This updated model is formulated as a set of nonlinear partial differential equations under the category of reaction-diffusion models, aiming to provide a more accurate representation of the dynamics and interactions involved in spreading infectious diseases in a given population. The methodology employed involves a comprehensive analysis of the master model system’s qualitative characteristics, focussing on the stability of its constituent subsystems. The model’s dynamical system is subjected to numerical solutions, enabling a detailed exploration of its behaviour under various conditions. A rigorous parametric variation is carried out to understand the model’s response to different parameter values. The novelty of this research is rooted in its pioneering approach to bridging the gap between theory and real-world observations. By rigorously validating theoretical results against empirical experimental data, the research aims to provide valuable insights into the dynamics of the ongoing pandemic. The outcomes generated by the present model system are expected to offer a deeper and more comprehensive understanding of the pandemic’s behaviour and transmission patterns, playing a pivotal role in advancing the field of theoretical modelling.

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Data Availability Statement

Data sharing does not apply to this article as no dataset and code were generated or analysed during the present study.

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Acknowledgements

In light of the improvement of the manuscript in its present revised version, the anonymous reviewers are gratefully acknowledged by the author for their invaluable comments and suggestions.

Funding

No funding received from any source to carry out this research work.

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Authors and Affiliations

  1. Department of Mathematics, School of Engineering and Applied Sciences, SRM University AP, Amaravati, Andhra Pradesh, 522240, India

    Koyel Chakravarty

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  1. Koyel Chakravarty
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Correspondence to Koyel Chakravarty.

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Appendix

Appendix

See Figs. 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48 and 49.

The figures representing the influence of significant model parameters are the following:

Fig. 37
figure 37

Time-series depictions of susceptible population subject to a discrete variation of \({\beta }_I\) and b continuous variation over the range of values of \({\beta }_I\)

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Fig. 38
figure 38

Time-series illustrations for susceptible population with comorbidity subject to a discrete variation of \({\beta }_{IC}\) and b continuous variation over the range of values of \({\beta }_{IC}\)

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Fig. 39
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Time-series representations for exposed population subject to a discrete variation of \({\beta }_I\) and b continuous variation over the range of values of \({\beta }_I\)

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Time-series representations for exposed population subject to a discrete variation of \({\beta }_{IC}\) and b continuous variation over the range of values of \({\beta }_{IC}\)

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Time-variant depictions for quarantined susceptible population with symptoms of fever subject to a discrete variation of \({\beta }_f\) and b continuous variation over the range of values of \({\beta }_f\)

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Fig. 42
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Time-series representations for quarantined exposed population subject to a discrete variation of \({\beta }_I\) and b continuous variation over the range of values of \({\beta }_I\)

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Time-series delineations for diagnosed and hospitalised population subject to a discrete variation of \({\delta }_I\) and b continuous variation over the range of values of \({\delta }_I\)

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Time-series delineations for diagnosed and hospitalised population subject to a discrete variation of \({\delta }_Q\) and b continuous variation over the range of values of \({\delta }_Q\)

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Time-series delineations for recovered population subject to a discrete variation of \(\gamma \) and b continuous variation over the range of values of \(\gamma \)

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Fig. 46
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Time-series delineations for vaccinated population subject to a discrete variation of \(\xi \) and b continuous variation over the range of values of \(\xi \)

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Fig. 47
figure 47

Time-series delineations for COVID Positive and Hospitalised population subject to a discrete variation of \(\alpha \) and b continuous variation over the range of values of \(\alpha \)

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Fig. 48
figure 48

Time-series delineations for symptomatic infected population subject to a discrete variation of \(\alpha \) and b continuous variation over the range of values of \(\alpha \)

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Fig. 49
figure 49

Time-series delineations for quarantined infected population subject to a discrete variation of \(\alpha \) and b continuous variation over the range of values of \(\alpha \)

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Chakravarty, K. The effect of vaccination on COVID-19 transmission dynamics with comorbidity using reaction–diffusion model. Eur. Phys. J. Plus 138, 1140 (2023). https://doi.org/10.1140/epjp/s13360-023-04766-9

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