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Dynamics of an \({ SVEIRS}\) Epidemic Model with Vaccination and Saturated Incidence Rate

  • Kunwer Singh Mathur
  • Prakash Narayan
Original Paper
  • 28 Downloads

Abstract

Measles and influenza are two major diseases–caused an epidemic in India. Therefore, in this paper, a \({ SVEIRS}\) epidemic mathematical model for measles and influenza is proposed and analyzed, where pre and post vaccinations are considered as control strategies with waning natural, vaccine-induced immunity and saturation incidence rate. The dissection of the proposed model is conferred in terms of the associated reproduction number \({\mathcal {R}}_v\), which is determined by the next-generation approach and obtained that if \({\mathcal {R}}_v\le 1\), the disease-free equilibrium exists and it is locally as well as globally asymptotically stable. Further for \({\mathcal {R}}_v> 1\), a unique endemic equilibrium exists and it is also locally as well as globally asymptotically stable under certain conditions, which shows the prevalence and persistence of the disease in the population.

Keywords

Pre and post vaccinations Reproduction number Saturated incidence rate Global stability 

Notes

Acknowledgements

We are very thankful to the anonymous referees and the editor in chief for their careful reading, constructive criticisms, helpful comments, and valuable suggestions, which have helped us to improve the quality of this work significantly.

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Copyright information

© Springer Nature India Private Limited 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsDr. Harisingh Gour VishwavidyalayaSagarIndia

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