Geometrical Methods and Numerical Computations for Prey-Predator Systems

Feedback Linearization and Optimal Control of the Kermack-McKendrick Model for the Spread of Epidemics

“…The results could be used both for the three-dimensional Kermack-McKendrick model and for further generalizations. A similar study for Lotka-Volterra systems was carried out by Ionescu and Munteanu in [1], [2].…”

“…This analysis is based on the application of various notions from the theory of dynamical systems to the numerical approximation of initial value problems over long time intervals. There is a strong interplay between the theory and the computational analysis of dynamical systems ( [1], [16], [17], [18], [19], [20]). In [1], [2], [21] a study of the Lotka-Volterra equations by geometrical tools was carried out, using the Hamilton-Poisson structures of this system of ordinary differential equations.…”

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“…Mathematical epidemic dynamics modeling can undoubtedly benefit largely from this accumulated expertise! In summary, it is therefore believed that first translating epidemic dynamics models into an analytical mechanics setting (related steps towards this aim may be found, e.g., in [Militaru and Munteanu 2013;Ionescu et al 2015;Seroussi et al 2019]) and then, secondly, exploiting the analogy between the two approaches while utilizing the full toolset of mechanical modeling can provide novel vistas and unprecedented opportunities. The present contribution aims to sketch out a few of these perspectives and to encourage the mechanics community to offer its strong modeling expertise to possibly and hopefully help further improve epidemic dynamics modeling.…”

Preservation of the invariants of Lotka-Volterra equations by iterated deferred correction methods

“…We consider the 3D LVS (3) on the interval [0, 100], with the parameter values (a, b, c, λ, µ, ν) = (−1, −1, −1, 0, 1, −1) [21]. The initial condition is taken as (u 1 (0), u 2 (0), u 3 (0)) T = (1, 1.9, 0.5) T .…”

“…They can be written as Poisson systems in bi-Hamiltonian form [17] and Nambu systems [18]. Many numerical methods are applied to LVSs which preserve the integrals, periodic solution, attractors and son on [6,19,20,21,22,23].…”