In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), and vaccinated (V). Initially, a mathematical analysis is carried out to illustrate the non-negativity, boundedness, epidemic equilibrium, existence, and uniqueness of the endemic equilibrium, and the basic reproduction number of the proposed model. Such numerical models can be, however, subject to various sources of uncertainties, due to an imperfect description of the biological processes governing the disease spread, which may strongly limit their forecasting skills. A data assimilation method, mainly, the ensemble Kalman filter (EnKF), is then used to constrain the model outputs and its parameters with available data. We conduct joint state-parameters estimation experiments assimilating daily data into the proposed model using the EnKF in order to enhance the model’s forecasting skills. Starting from the estimated set of model parameters, we then conduct short-term predictions in order to assess the predicability range of the model. We apply the proposed assimilation system on real data sets from Saudi Arabia. The numerical results demonstrate the capability of the proposed model in achieving accurate prediction of the epidemic development up to two-week time scales. Finally, we investigate the effect of vaccination on the spread of the pandemic.

In this paper, a mathematical model was developed to simulate SARS-CoV-2 dynamics in infected patients. The model considers both the innate and adaptive immune responses and consists of healthy cells, infected cells, viral load, cytokines, natural killer cells, cytotoxic T-lymphocytes, B-lymphocytes, plasma cells, and antibody levels. First, a mathematical analysis was performed to discuss the model’s equilibrium points and compute the basic reproduction number. The accuracy of such mathematical models may be affected by many sources of uncertainties due to the incomplete representation of the biological process and poorly known parameters. This may strongly limit their performance and prediction skills. A state-of-the-art data assimilation technique, the ensemble Kalman filter (EnKF), was then used to enhance the model’s behavior by incorporating available data to determine the best possible estimate of the model’s state and parameters. The proposed assimilation system was applied on the real viral load datasets of six COVID-19 patients. The results demonstrate the efficiency of the proposed assimilation system in improving the model predictions by up to $40\%$.

In this paper, supplementary cementitious materials are used as a substitute for cement to decrease carbon dioxide emissions. A by-product of the iron manufacturing industry, ground granulated blast-furnace slag (GGBS), known to improve some performance characteristics of concrete, is used as an effective cement replacement to manufacture mortar samples. Here, the influence of curing conditions on the durability of samples including various amounts of GGBS is investigated experimentally and numerically. Twelve high-strength Portland cement CEM I 52.5 N samples were prepared, in which 0%, 45%, 60%, and 80% of cement were substituted by GGBS. In addition, three curing conditions (standard, dry, and cold curing) were applied to the samples. Durability aspects were studied through porosity, permeability, and water absorption. Experimental results indicate that samples cured in standard conditions gave the best performance in comparison to other curing conditions. Furthermore, samples incorporating $45\%$ of GGBS have superior durability properties. Permeability and water absorption were improved by $17\%$ and $18\%$, respectively, compared to the reference sample. Thereafter, data from capillary suction experiments were used to numerically determine the hydraulic properties based on a Bayesian inversion approach, namely the Markov Chain Monte Carlo method. Finally, the developed numerical model accurately estimates the hydraulic characteristics of mortar samples and greatly matches the measured water inflow over time through the samples.