Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments

Pritam Saha, Bapin Mondal and Uttam Ghosh

Chaos, Solitons & Fractals, 2023, vol. 174, issue C

Abstract: This manuscript deals with an epidemic model with partial immunity having nonlinear incidence and saturated treatment. Positivity and boundedness of the solutions have been established here. We discuss local stability of all equilibria. The proposed system experiences various types of bifurcations, namely Transcritical, Saddle–node, Hopf, and Bogdanov–Takens bifurcation of co-dimension 2. The system is reduced to a two-dimensional system using center manifold theorem to deduce normal form for Bogdanov–Takens bifurcation of co-dimension 2 when two eigenvalues at the endemic equilibrium point becomes zero. Whether deterministic model overestimates the condition for disease propagation, to observe this we also analysis stochastic model. We derive the condition for extinction, persistence in mean and stationary distribution. All theoretical findings are justified by numerical simulations. Finally, to check validity of the model, we fit it with real reported influenza data of Canada.

Keywords: Center manifold theorem; Bogdanov–Takens bifurcation; Persistence in mean; Stationary distribution; Model validation (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923006768

DOI: 10.1016/j.chaos.2023.113775

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