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

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.

Mathematical Modeling of the Infectious Diseases: Key Concepts and Applications

“…The stochastic models represent a more realistic approach to model infectious diseases because they contemplate the high degree of uncertainty in the dynamics of transmission, providing a range of possible outcomes of an outbreak considering a large number of variables that influence the epidemic behavior of an infectious disease, however, they tend to be limited regarding the degree of complexity in the formulation of the mathematical system and data interpretation through different methods, such as the use of master equations [28], itô calculations [29], as well as other mathematical and statistical approaches based on brownian motion [30], or markov processes that add stochasticity to differen-…”

“…Highlighting the model's parameter were evaluated using the maximum-likelihood adopting 95% of confidence interval, then sets of parameters generated by latin hypercube sampling were computed assuming twice the difference of log-likelihood values that was X 2 distributed with degrees of freedom with values equal to the number of estimated parameters, then 700 simulations were run by the gillespie's first reaction method, and in each simulation, the partial rank correlation coefficient was computed to analyze the influence of each parameter in the epidemic size. [21,22,29,45], by the exponential growth rate method and maximum likelihood method [17], or by bayesian statistics [46]. Moreover, the R0 is a parameter used to evaluate the efficacy of interventions such as quarantine, mask-wearing, vaccination, washing hands in hospital sets, among others; where if the intervention decreases the R0 to values smaller than 1, it is considered effective, and uneffective if it does not change the R0 [7,[47][48][49].…”

Forecasting daily new infections, deaths and recovery cases due to COVID-19 in Pakistan by using Bayesian Dynamic Linear Models

“…In the current pandemics, to model and forecast new infections, deaths and recoveries due to COVID-19, different researchers have used different techniques including statistical, mathematical, machine learning algorithm, deep learning etc. [17][18][19][20][21]. [21] compared six time series models, including ARIMA [7], the Holt-Winters additive model (HWAAS) [22], TBAT [23], Facebook's Prophet [24], DeepAR [25] and N-Beats [26].…”

Hybrid Method for Simulation of a Fractional COVID-19 Model with Real Case Application

“…The work in [5] studies the COVID-19 pandemic in Portugal until the end of the three states of emergency, describing well what has happen in Portugal with respect to the evolution of active infected and hospitalized individuals. In [6,7], a non-fractional but stochastic time-delayed model for COVID-19 is given, with the aim to study the situation of Morocco. In [8], the authors provide a S-E-I-P-A-H-R-F model while here we propose a much simpler P-I-Q model (our model has only three state variables while the model in [8] is much more complex, with eight state variables).…”