Understanding and forecasting the progression of disease epidemics is possible through the study of nonlinear epidemic biochemical models that describe the relationship among susceptible, infected, and immune individuals in a population. In this paper, by determining the algebraic invariant planes and studying the Hopf bifurcation on these invariant planes, we study the stability of the Hopf bifurcation in the infection-free and endemic states of the SIR and SIRS epidemic models with bilinear incidence rate. We analyze the stability of the limit cycles of the bilinear incidence SIR and SIRS models at the steady state point where infection vanishes and at the endemic steady state point where the system behaves in an oscillatory manner. We demonstrate the algebraic results by numerical simulations for parameter values that satisfy the conditions for both free and endemic states.
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September 2023
Research Article|
September 15 2023
Biochemical models of SIR and SIRS: Effects of bilinear incidence rate on infection-free and endemic states
Orhan Ozgur Aybar
Orhan Ozgur Aybar
a)
(Conceptualization, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – review & editing)
Department of Mathematics, Faculty of Art and Sciences, Piri Reis University
, Tuzla, Istanbul 34940, Turkey
and Computational Science and Engineering Program, Institute of Graduate Studies, Piri Reis University
, Tuzla, Istanbul 34940, Turkey
a)Author to whom correspondence should be addressed: oaybar@pirireis.edu.tr
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a)Author to whom correspondence should be addressed: oaybar@pirireis.edu.tr
Chaos 33, 093120 (2023)
Article history
Received:
July 04 2023
Accepted:
August 28 2023
Citation
Orhan Ozgur Aybar; Biochemical models of SIR and SIRS: Effects of bilinear incidence rate on infection-free and endemic states. Chaos 1 September 2023; 33 (9): 093120. https://doi.org/10.1063/5.0166337
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