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Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can't be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. [ABSTRACT FROM AUTHOR]

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. • SIRS model with logistic growth, saturated type incidence and treatment. • Bogdanov–Takens bifurcation normal form using Center manifold theorem. • Introduction of stochasticity in the model and it's analysis. • Model is validated fitting with real influenza outbreak data of Canada. [ABSTRACT FROM AUTHOR]