Mathematical Modeling of Immune Responses against SARS-CoV-2 Using an Ensemble Kalman Filter

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%.

Natural processes dominate the pollution levels during COVID-19 lockdown over India.

The lockdown measures that were taken to combat the COVID-19 pandemic minimized anthropogenic activities and created natural laboratory conditions for studying air quality. Both observations and WRF-Chem simulations show a 20-50% reduction (compared to pre-lockdown and same period of previous year) in the concentrations of most aerosols and trace gases over Northwest India, the Indo Gangetic Plain (IGP), and the Northeast Indian regions. It is shown that this was mainly due to a 70-80% increase in the height of the boundary layer and the low emissions during lockdown. However, a 60-70% increase in the pollutants levels was observed over Central and South India including the Arabian sea and Bay of Bengal during this period, which is attributed to natural processes. Elevated (dust) aerosol layers are transported from the Middle East and Africa via long-range transport, and a decrease in the wind speed (20-40%) caused these aerosols to stagnate, enhancing the aerosol levels over Central and Southern India. A 40-60% increase in relative humidity further amplified aerosol concentrations. The results of this study suggest that besides emissions, natural processes including background meteorology and dynamics, play a crucial role in the pollution concentrations over the Indian sub-continent.

An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter

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.