Three Mathematical Models for COVID-19 Prediction

The COVID-19 outbreak was a major event that greatly impacted the economy and the health systems around the world. Understanding the behavior of the virus and being able to perform long-term and short-term future predictions of the daily new cases is a working field for machine learning methods and mathematical models. This paper compares Verhulst's, Gompertz´s, and SIR models from the point of view of their efficiency to describe the behavior of COVID-19 in Spain. These mathematical models are used to predict the future of the pandemic by first solving the corresponding inverse problems to identify the model parameters in each wave separately, using as observed data the daily cases in the past. The posterior distributions of the model parameters are then inferred via the Metropolis-Hastings algorithm, comparing the robustness of each prediction model and making different representations to visualize the results obtained concerning the posterior distribution of the model parameters and their predictions. The knowledge acquired is used to perform predictions about the evolution of both the daily number of infected cases and the total number of cases during each wave. As a main conclusion, predictive models are incomplete without a corresponding uncertainty analysis of the corresponding inverse problem. The invariance of the output (posterior prediction) with respect to the forward predictive model that is used shows that the methodology shown in this paper can be used to adopt decisions in real practice (public health).

Analysis of transcriptomic responses to SARS-CoV-2 reveals plausible defective pathways responsible for increased susceptibility to infection and complications and helps to develop fast-track repositioning of drugs against COVID-19.

BACKGROUND: To understand the transcriptomic response to SARS-CoV-2 infection, is of the utmost importance to design diagnostic tools predicting the severity of the infection. METHODS: We have performed a deep sampling analysis of the viral transcriptomic data oriented towards drug repositioning. Using different samplers, the basic principle of this methodology the biological invariance, which means that the pathways altered by the disease, should be independent on the algorithm used to unravel them. RESULTS: The transcriptomic analysis of the altered pathways, reveals a distinctive inflammatory response and potential side effects of infection. The virus replication causes, in some cases, acute respiratory distress syndrome in the lungs, and affects other organs such as heart, brain, and kidneys. Therefore, the repositioned drugs to fight COVID-19 should, not only target the interferon signalling pathway and the control of the inflammation, but also the altered genetic pathways related to the side effects of infection. We also show via Principal Component Analysis that the transcriptome signatures are different from influenza and RSV. The gene COL1A1, which controls collagen production, seems to play a key/vital role in the regulation of the immune system. Additionally, other small-scale signature genes appear to be involved in the development of other COVID-19 comorbidities. CONCLUSIONS: Transcriptome-based drug repositioning offers possible fast-track antiviral therapy for COVID-19 patients. It calls for additional clinical studies using FDA approved drugs for patients with increased susceptibility to infection and with serious medical complications.

Predictive Mathematical Models of the Short-Term and Long-Term Growth of the COVID-19 Pandemic.

The prediction of the dynamics of the COVID-19 outbreak and the corresponding needs of the health care system (COVID-19 patients' admissions, the number of critically ill patients, need for intensive care units, etc.) is based on the combination of a limited growth model (Verhulst model) and a short-term predictive model that allows predictions to be made for the following day. In both cases, the uncertainty analysis of the prediction is performed, i.e., the set of equivalent models that adjust the historical data with the same accuracy. This set of models provides the posterior distribution of the parameters of the predictive model that adjusts the historical series. It can be extrapolated to the same analyzed time series (e.g., the number of infected individuals per day) or to another time series of interest to which it is correlated and used, e.g., to predict the number of patients admitted to urgent care units, the number of critically ill patients, or the total number of admissions, which are directly related to health needs. These models can be regionalized, that is, the predictions can be made at the local level if data are disaggregated. We show that the Verhulst and the Gompertz models provide similar results and can be also used to monitor and predict new outbreaks. However, the Verhulst model seems to be easier to interpret and to use.