Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers. (7th June 2022)

• Record Type: Journal Article
• Authors: Haas, F; Kröger, M; Schlickeiser, R
• Is Part Of: Journal of physics. Volume 55:Number 22(2022)
• Publication Date: 2022-06-07
• Subjects: corona virus -- Poisson structure -- super-integrable system -- epidemics -- Nambu mechanics -- Covid-19; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac6995
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We derive a generalized Hamiltonian formalism for a modified susceptible–infectious–recovered/removed (SIR) epidemic model taking into account the population V of vaccinated persons. The resulting SIRV model is shown to admit three possible functionally independent Hamiltonians and hence three associated Poisson structures. The reduced case of vanishing vaccinated sector shows a complete correspondence with the known Poisson structures of the SIR model. The SIRV model is shown to be expressible as an almost Nambu system, except for a scale factor function breaking the divergenceless property. In the autonomous case with time-independent stationary ratios k and b, the SIRV model is shown to be a maximally super-integrable system. For this case we test the accuracy of numerical schemes that are suited to solve the stiff set of SIRV differential equations.