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SeMA Journal

pp 1–15 | Cite as

A short study of an SIR model with inclusion of an alert class, two explicit nonlinear incidence rates and saturated treatment rate

  • Abhishek Kumar
  • NilamEmail author
  • Raj Kishor
Article
  • 16 Downloads

Abstract

In this paper, we present a susceptible–alert–infected–recovered (SAIR) epidemic model with the consideration of two explicit saturated incidence rates and Holling functional type II treatment rate. Awareness about the epidemic may play a vital role in the control of the spread of an epidemic. Hence, an alert compartment has been incorporated into the model. It strives us to take two incidence rates: one from the susceptible class to infected class and another from alert class to infected class. Holling functional type II treatment rate has been introduced to capture the effects of resource limitation in treating infectives. The model has a disease-free equilibrium (DFE), which is locally asymptotically stable when \( R_{0} < 1 \). Using the center manifold theory, we show that DFE exhibits the forward bifurcation at \( R_{0} = 1 \). Stability of the endemic equilibrium has also been analyzed and discussed. Numerical simulations have been done by MATLAB 2012b and the outcomes have been discussed with the help of graphs in the paper.

Keywords

Epidemic SAIR model Saturated treatment rate Basic reproduction number Center manifold theory Stability 

Mathematics Subject Classification

34D20 92B05 37M05 

Notes

Acknowledgements

The authors are thankful to Delhi Technological University, Delhi, for monetary support for this research. The authors also gratefully acknowledge the handling editor and anonymous reviewers for their valuable suggestions which enhance the quality of the paper.

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Copyright information

© Sociedad Española de Matemática Aplicada 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsDelhi Technological UniversityDelhiIndia
  2. 2.Raj TutorsBijnorIndia

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