Epidemics control model with consideration of seven-segment population model

Abstract

This paper discusses a novel method for modeling the spread of an epidemic that facilitates the calculation of the optimal control policy. The proposed model considers seven compartments in the population as opposed to popular approaches based on three or four compartments. The usual compartments, i.e., susceptible, exposed, infected, and recovered individuals have been included in the seven compartment model with the addition of compartments pertaining to individuals under treatment, vaccinated individuals, and individuals in quarantine. The addition of new compartments allows for the incorporation of multiple control options such as treatment, quarantine, and vaccination. The mathematical expressions involved in the model have been described followed by a discussion on the calculation of optimal control policy. Finally, a simulation-based example has been included for demonstrating the effectiveness of the control policy resulting from the proposed model.

A Markovian Model for the Spread of the SARS-CoV-2 Virus

“…An interesting example is the work of Viet et al [30], in which the authors use an MDP to model the spread of the Porcine Reproductive and Respiratory Syndrome (PPRS) and use it to synthesise a regional policy for its containment. A similar attempt has been made also for the SARS-CoV-2 by Nasir et al [25]. The authors consider a segmented model for the population and model its evolution via a MDP with the purpose of synthesising an optimal policy for vaccination, hospitalisation and quarantine.…”

“…Our work lies in this line of research. As in [25], we show how to construct a MDP describing the SARS-CoV-2 epidemics using a segmented model for the population, but our model is very detailed and contains an exhaustive discussion on how to compute the transition probabilities and on how to use the model for control design and analysis. Very interestingly, Nasir et al [25] discuss in alarming terms the problem of scalability of epidemic models based on MDPs.…”

“…As in [25], we show how to construct a MDP describing the SARS-CoV-2 epidemics using a segmented model for the population, but our model is very detailed and contains an exhaustive discussion on how to compute the transition probabilities and on how to use the model for control design and analysis. Very interestingly, Nasir et al [25] discuss in alarming terms the problem of scalability of epidemic models based on MDPs. The technique that they suggest to deal with large populations is by abstraction, i.e., by considering a unit of population in the model as the representative of a number of people.…”

“…These experiments have been carried out with a small population. However, we remark that the population can be scaled using quantisation, as in [25]. The price to pay in this case is an accuracy reduction due to the quantisation error.…”

“…The study of larger populations using the presented model is possible in different ways. A first possibility, discussed in the related work section, is by exploiting some recent results on scalable techniques for MDP analysis and design [25,17]. Another possibility is by using a small size population model to develop a policy with guaranteed properties, and then recover the result on a heuristic basis for larger populations verifying its efficacy through Monte Carlo simulations, as shown in this paper.…”