Optimal control of a probabilistic dynamic for epidemic spreading in arbitrary complex networks

TL;DR

This paper develops a probabilistic dynamic model for epidemic spreading on complex networks and derives optimal control strategies for vaccination and hospitalization using Pontryagin's maximum principle, supported by numerical simulations.

Contribution

It introduces a discrete-time Markov chain model for epidemic spread and formulates optimal control policies for vaccination and hospitalization.

Findings

Optimal control strategies are derived for epidemic mitigation.

Numerical simulations demonstrate effectiveness of control policies.

Model captures contact-based epidemic dynamics on complex networks.

Abstract

This paper presents a discrete time probabilistic dynamic for simulating a contact-based epidemic spreading based on discrete time Markov chain process, in particular the attention is addressed to the susceptible-infectious-removed (SIR) model and the phase diagram of such model will be presented. Then, this report presents the set of equations that represent the optimal control strategies, by the means of Pontryagin's maximum principle, in two different cases a vaccination policy and a combined vaccination-hospitalization policy and show a numerical simulation, with the standard forward-backward sweep procedure, for these equations.