Modeling and Forecasting of COVID-19 Spreading by Delayed Stochastic Differential Equations

TL;DR

This paper extends traditional SIR models to include stochastic and delayed elements to better predict COVID-19 spread in Morocco, evaluating the impact of preventive measures through real data and simulations.

Contribution

It introduces delayed stochastic differential equations into COVID-19 modeling, providing a novel framework for understanding disease dynamics with real data validation.

Findings

Models are well-posed with conditions for disease extinction or persistence.

Parameter estimation from real data enhances forecast accuracy.

Numerical simulations validate theoretical results and forecast trends.

Abstract

The novel coronavirus disease (COVID-19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID-19 in Morocco was reported on 2 March 2020, and the number of reported cases has increased day by day. In this work, we extend the well-known SIR compartmental model to deterministic and stochastic time-delayed models in order to predict the epidemiological trend of COVID-19 in Morocco and to assess the potential role of multiple preventive measures and strategies imposed by Moroccan authorities. The main features of the work include the well-posedness of the models and conditions under which the COVID-19 may become extinct or persist in the population. Parameter values have been estimated from real data and numerical simulations are presented for forecasting the COVID-19 spreading as well as verification of theoretical results.