Bifurcations analysis of a discrete time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e337" altimg="si1.svg"><mml:mrow><mml:mi>S</mml:mi><mml:mi>I</mml:mi><mml:mi>R</mml:mi></mml:mrow></mml:math> epidemic model with nonlinear incidence function
Reny George, Nadia Gul, Anwar Zeb, Z. Avazzadeh, Salih Djilali, Shahram Rezapour
Abstract
In this paper, we present a discrete-time SIR epidemic model and investigate the stability of its fixed points, as well as the bifurcations of the one and two parameters. The numerical normal form is used to analyze bifurcations. This model exhibits Neimark–Sacker transcritical, flip, and strong resonance bifurcations. Using the critical coefficients, a scenario is identified for each bifurcation. We verify analytical results using the MATLAB package MatContM, which employs the numerical continuation method.
Topics & Concepts
MATLABBifurcationStability (learning theory)Discrete time and continuous timeApplied mathematicsNumerical analysisMathematicsComputer scienceAlgorithmMathematical analysisStatisticsPhysicsMachine learningProgramming languageQuantum mechanicsNonlinear systemMathematical and Theoretical Epidemiology and Ecology ModelsFractional Differential Equations SolutionsCOVID-19 epidemiological studies