Continuous-time stochastic processes for the spread of COVID-19 disease simulated via a Monte Carlo approach and comparison with deterministic models

Abstract

Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible S, infected I, removed R and dead people D. In order to have a cross validation, a deterministic version of such a model is also devised which is represented by a system of ordinary differential equations with delays. In the second stochastic model two further compartments are added: the class A of asymptomatic individuals and the class L of isolated infected people. Effects such as social distancing measures are easily included and the consequences are analyzed. Numerical solutions are obtained with Monte Carlo simulations. Quantitative predictions are provided which can be useful for the evaluation of political measures, e.g. the obtained results suggest that strategies based on herd immunity are too risky. Finally, the models are calibrated on data referring to the second wave of infection in Italy.

A Time-Delayed Deterministic Model for the Spread of COVID-19 with Calibration on a Real Dataset

“…If the class of dead (D) people is also considered, the model takes the name of SIRD. Since COVID-19 has a relevant incubation period [18] and an identifiable period from infection to recovery [19], in [7], a SIRD model with time delays has been proposed as follows.…”

“…Epidemic models based on ordinary differential equations have been introduced in [2,4,5]. Stochastic models have been proposed in [6,7]. For models based on stochastic differential equations, see, e.g., [8,9].…”

“…In [7] a deterministic model based on differential equations with time delays has been devised, although it was introduced only to validate the stochastic one and no applications have been provided by using such a model. In [12,13], mathematical models with only a delay regarding the incubation time are presented.…”

A Continuous-Time Markov Chain Model for the Spread of COVID-19

“…In conclusion, the model considered here is a good pedagogical starting point for students to apply their coursework to COVID-19 data. Further, the present time is opportune for motivating students and faculty to read ongoing research on modelling the spread of COVID-19 and other infectious diseases; cf., Calleri, et al [3], Oraby, et al [8].…”

Well-posedness for a diffusion-reaction compartmental model simulating the spread of COVID-19

“…The COVID-19 outbreak that deeply affected the world starting from the first months of 2020 led to a new, strong interest by researchers towards the development of mathematical models of infectious diseases, allowing the assessment of different scenarios and aiming at assisting the complex political decision-making process during the pandemic. As a consequence, many papers were recently published, proposing interesting modeling ideas (see, e.g., [1,9,12,13,17,18,20,23,25]), often based on compartmental models, where the considered population is divided into "compartments" based on their qualitative characteristics (like, e.g., "susceptible", "infected", "recovered"), with different assumptions about the nature and rate of transfer across compartments. Despite this kind of models do not readily offer the possibility of a multiscale vision (as, e.g., proposed in [3]), that would be a preferred feature given the nature of the phenomena to be simulated, they have the advantage of allowing a relatively easy introduction of diffusion terms (in this context, compelling ideas on diffusion models can be found, among others, in [4,5,24] and references therein).…”