We derive a novel model escorted by large scale compartments, based on a set of coupled delay differential equations with extensive delays, in order to estimate the incubation, recovery and decease periods of COVID-19, and more generally any infectious disease. This is possible thanks to some optimization algorithms applied to publicly available database of confirmed corona cases, recovered cases and death toll. In this purpose, we separate (1) the total cases into 14 groups corresponding to 14 incubation periods, (2) the recovered cases into 406 groups corresponding to a combination of incubation and recovery periods, and (3) the death toll into 406 groups corresponding to a combination of incubation and decease periods. In this paper, we focus on recovery and decease periods and their correlation with the incubation period. The estimated mean recovery period we obtain is 22.14 days (95% Confidence Interval (CI) 22.00–22.27), and the 90th percentile is 28.91 days (95% CI 28.71–29.13), which is in agreement with statistical supported studies. The bimodal gamma distribution reveals that there are two groups of recovered individuals with a short recovery period, mean 21.02 days (95% CI 20.92–21.12), and a long recovery period, mean 38.88 days (95% CI 38.61–39.15). Our study shows that the characteristic of the decease period and the recovery period are alike. From the bivariate analysis, we observe a high probability domain for recovered individuals with respect to incubation and recovery periods. A similar domain is obtained for deaths analyzing bivariate distribution of incubation and decease periods.

We propose a novel model based on a set of coupled delay differential equations with fourteen delays in order to accurately estimate the incubation period of COVID-19, employing publicly available data of confirmed corona cases. In this goal, we separate the total cases into fourteen groups for the corresponding fourteen incubation periods. The estimated mean incubation period we obtain is 6.74 days (95% Confidence Interval(CI): 6.35 to 7.13), and the 90th percentile is 11.64 days (95% CI: 11.22 to 12.17), corresponding to a good agreement with statistical supported studies. This model provides an almost zero-cost computational complexity to estimate the incubation period.

In this paper, we derive and analyze an extended SIRS-model which includes lockdown policies at the early stages of the pandemic. The latter play a salient role for flattening the curve of infectious diseases such as COVID-19, and is introduced as a model compartment. An error function is reported, which serves as a bridge between the outcomes of the model and available databases; we estimate the values of the model parameters by minimizing the error function. The intervention function, obtained from the equivalent system of the proposed model, and effective reproduction function are also derived to understand the underline scenario of the coronavirus outbreak. We then estimate the epidemiological variables such as susceptible, recovered, lockdown etc. for Canada and three of its provinces, Ontario, Qu\’ebec and British Columbia, significantly affected by the coronavirus. Some improvements, such as spatial dependence or “at risk’‘ vs “healthy” population, will finally be proposed in order to increase the accuracy of the modeling.

We derive a novel hybrid approach, a combination of neural networks and inverse problem, in order to forecast COVID-19 cases, and more generally any infectious disease. For this purpose, we extract a second order nonlinear differential equation for the total confirmed cases from a SIR-like model. The latter is the cornerstone of the present study which allows to rigorously simplify the construction of the time-dependent epidemiological parameters without solving a system of differential equations. The neural network and inverse problems are used to compute the trial functions for total cases and the model parameters, respectively. The number of suspected and infected individuals can be found using the trial function of total confirmed cases. We divide the time domain into two parts, training interval (first 365/395 days) and test interval (first 366 to 395/ 396 to 450 days), and train the neural networks on the preassigned training zones. To examine the efficiency and effectiveness, we apply the proposed method to Canada, and use the Canadian publicly available database to estimate the parameters of the trial function involved with total cases. The trial functions of model parameters show that the basic reproduction number was closed to unity over a wide range, the first 100 to 365 days of the current pandemic in Canada. The proposed prediction models, based on the influence of previous COVID-19 cases and social economic policy, show excellent agreement with the data. The test results reveal that the single path prediction can forecast a period of 30 days, and the prediction using previous social and economical situation can forecast a range of 55 days.

We propose an original model based on a set of coupled delay differential equations with fourteen delays in order to accurately estimate the incubation period of COVID-19, employing publicly available data of confirmed corona cases. In this goal, we separate the total cases into fourteen groups for the corresponding fourteen incubation periods. The estimated mean incubation period we obtain is 6.74 days (95% Confidence Interval(CI): 6.35 to 7.13), and the 90th percentile is 11.64 days (95% CI: 11.22 to 12.17), corresponding to a good agreement with statistical supported studies. This model provides an almost zero-cost approach to estimate the incubation period.