| We derive a generalized Hamiltonian formalism for a modified suscepti- ble.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 sys- tem, 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.
for LaTeX users @article{FHaas2022-55,
author = {F. Haas and M. Kr\"oger and R. Schlickeiser},
title = {Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers},
journal = {J. Phys. A},
volume = {55},
pages = {225206},
year = {2022}
}
\bibitem{FHaas2022-55} F. Haas, M. Kr\"oger, R. Schlickeiser,
Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers,
J. Phys. A {\bf 55} (2022) 225206.FHaas2022-55
F. Haas, M. Kr\"oger, R. Schlickeiser
Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers
J. Phys. A,55,2022,225206 |
mk@mat.ethz.ch
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