Modeling epidemics through ladder operators

TL;DR

This paper introduces a novel operator-based model for epidemic spreading that effectively reproduces long-term disease dynamics and assesses intervention impacts, such as lockdowns, on infection outcomes.

Contribution

It presents a new operator technique for modeling epidemics, providing a natural framework for interactions and transformations among population groups, and applies it successfully to real SARS and COVID-19 data.

Findings

Model accurately reproduces long-term epidemic behavior.

Lockdown measures significantly reduce the asymptotic number of infected.

The approach offers a flexible way to incorporate intervention strategies.

Abstract

We propose a simple model of spreading of some infection in an originally healthy population which is different from other models existing in the literature. In particular, we use an operator technique which allows us to describe in a natural way the possible interactions between healthy and un-healthy populations, and their transformation into recovered and to dead people. After a rather general discussion, we apply our method to the analysis of Chinese data for the SARS-2003 (Severe acute respiratory syndrome; SARS-CoV-1) and the Coronavirus COVID-19 (Corona Virus Disease; SARS-CoV-2 ) and we show that the model works very well in reproducing the long-time behaviour of the disease, and in particular in finding the number of affected and dead people in the limit of large time. Moreover, we show how the model can be easily modified to consider some lockdown measure, and we deduce that this procedure drastically reduces the asymptotic value of infected individuals, as expected, and observed in real life.