Path integral control of a stochastic multi-risk SIR pandemic model.

In this paper a Feynman-type path integral control approach is used for a recursive formulation of a health objective function subject to a fatigue dynamics, a forward-looking stochastic multi-risk susceptible-infective-recovered (SIR) model with risk-group's Bayesian opinion dynamics toward vaccination against COVID-19. My main interest lies in solving a minimization of a policy-maker's social cost which depends on some deterministic weight. I obtain an optimal lock-down intensity from a Wick-rotated Schrödinger-type equation which is analogous to a Hamiltonian-Jacobi-Bellman (HJB) equation. My formulation is based on path integral control and dynamic programming tools facilitates the analysis and permits the application of algorithm to obtain numerical solution for pandemic control model.

Spreading of Corona Virus in Central Europe: The Cases of Italy and Spain and the Very Beginning of Pandemic

In this paper a mathematical model that focuses at the very beginning of pandemic at Europe is presented. In essence it is assumed that once the virus arrived to Italy then the geographical propagation was done through probabilistic rules among then to Spain. Because of this the model of propagation of Feynman in conjunction to Wiener schemes have been used to model the displacement of virus from Wuhan to Milan as well from Milan to Spain, as seen at the end of 2019 triggering the beginning of European pandemic at January of 2020. As seen at official data Italy and Spain have presented same statistics at the first months of local pandemic. From the usage of the proposed formalism, it is found that the country data are following Gaussian-like distributions due to the space-time propagation of virus. © 2021 IEEE.