Network-based uncertainty quantification for mathematical models in epidemiology.

After the new Coronavirus disease (COVID-19) emerged in the end of January 2020 in Germany, a large number of individuals suffered from severe symptoms and eventually needed intensive care in hospitals. Due to the rapid spread of the disease, the number of deceased individuals increased as well, which is a motivation to prevent as many new infections as possible. Therefore, the knowledge about the current evolution of the virus spread is crucial to predict its future behavior and to react with suitable interventions. In this paper, the evolution of the COVID-19 pandemic in Germany is forecasted by a network-based inference method, in which the interactions of individuals are taken into account using a contact matrix. Then the results are compared to the predictions without considering a contact matrix as well as to the logistic regression, which shows the advantage of incorporating the contact matrix. Furthermore, the basic reproduction number of the pandemic in Germany using a neural network approach is estimated and used for further predictions of the evolution of COVID-19 in Germany. In order to mathematically model the different compartments of the population in the considered regions, the classical SIR model is employed. In this work, we deploy the LASSO (Least Absolute Shrinkage and Selection Operator) for the unknown parameter estimation. Furthermore, we calculate and illustrate the MAPE (Mean Absolute Percentage Error) of the estimations to show the accuracy of the predictions. The results include model parameter estimation and model validation, as well as the outbreak forecasting using network-informed algorithms. Our findings show that the network-inference based approach outperforms the logistic regression as well as the neural network approach and the SIR model calibration without a contact network. Furthermore according to the results, the network-inference based approach is particularly suitable for short- to mid-term predictions, even when there is not much information about the new disease. Moreover, the predictions based on the estimation of the reproduction number in Germany can yield more reliable results with increasing the availability of data, but could not outperform the network-inference based algorithm.

Uncertainty quantification in epidemiological models for the COVID-19 pandemic.

Mathematical modeling of epidemiological diseases using differential equations are of great importance in order to recognize the characteristics of the diseases and their outbreak. The procedure of modeling consists of two essential components: the first component is to solve the mathematical model numerically, the so-called forward modeling. The second component is to identify the unknown parameter values in the model, which is known as inverse modeling and leads to identifying the epidemiological model more precisely. The main goal of this paper is to develop the forward and inverse modeling of the coronavirus (COVID-19) pandemic using novel computational methodologies in order to accurately estimate and predict the pandemic. This leads to governmental decisions support in implementing effective protective measures and prevention of new outbreaks. To this end, we use the logistic equation and the SIR (susceptible-infected-removed) system of ordinary differential equations to model the spread of the COVID-19 pandemic. For the inverse modeling, we propose Bayesian inversion techniques, which are robust and reliable approaches, in order to estimate the unknown parameters of the epidemiological models. We deploy an adaptive Markov-chain Monte-Carlo (MCMC) algorithm for the estimation of a posteriori probability distribution and confidence intervals for the unknown model parameters as well as for the reproduction number. We perform our analyses on the publicly available data for Austria to estimate the main epidemiological model parameters and to study the effectiveness of the protective measures by the Austrian government. The estimated parameters and the analysis of fatalities provide useful information for decision-makers and makes it possible to perform more realistic forecasts of future outbreaks. According to our Bayesian analysis for the logistic model, the growth rate and the carrying capacity are estimated respectively as 0.28 and 14974. Moreover for the parameters of the SIR model, namely the transmission rate and recovery rate, we estimate 0.36 and 0.06, respectively. Additionally, we obtained an average infectious period of 17 days and a transmission period of 3 days for COVID-19 in Austria. We also estimate the reproduction number over time for Austria. This quantity is estimated around 3 on March 26, when the first recovery was reported. Then it decays to 1 at the beginning of April. Furthermore, we present a fatality analysis for COVID-19 in Austria, which is also of importance for governmental protective decision-making. According to our analysis, the case fatality rate (CFR) is estimated as 4% and a prediction of the number of fatalities for the coming 10 days is also presented. Additionally, the ICU bed usage in Austria indicates that around 2% of the active infected individuals are critical cases and require ICU beds. Therefore, if Austrian governmental protective measures would not have taken place and for instance if the number of active infected cases would have been around five times larger, the ICU bed capacity could have been exceeded.

Bayesian inversion for a biofilm model including quorum sensing.

We propose a mathematical model based on a system of partial differential equations (PDEs) for biofilms. This model describes the time evolution of growth and degradation of biofilms which depend on environmental factors. The proposed model also includes quorum sensing (QS) and describes the cooperation among bacteria when they need to resist against external factors such as antibiotics. The applications include biofilms on teeth and medical implants, in drinking water, cooling water towers, food processing, oil recovery, paper manufacturing, and on ship hulls. We state existence and uniqueness of solutions of the proposed model and implement the mathematical model to discuss numerical simulations of biofilm growth and cooperation. We also determine the unknown parameters of the presented biofilm model by solving the corresponding inverse problem. To this end, we propose Bayesian inversion techniques and the delayed-rejection adaptive-Metropolis (DRAM) algorithm for the simultaneous extraction of multiple parameters from the measurements. These quantities cannot be determined directly from the experiments or from the computational model. Furthermore, we evaluate the presented model by comparing the simulations using the estimated parameter values with the measurement data. The results illustrate a very good agreement between the simulations and the measurements.

Efficacy of Rose Oil Soft Capsules on Clinical Outcomes in Ulcerative Colitis: A Pilot Randomized, Double-Blinded, Placebo-Controlled Clinical Trial.

BACKGROUND: Ulcerative colitis is the most common form of inflammatory bowel disease worldwide, which presents with superficial ulcers in the rectum and colon. The aim of this study was to assess the effectiveness of rose oil soft capsules over placebo on the clinical outcomes in moderate to severe ulcerative colitis. MATERIALS AND METHODS: This study was a pilot randomized, double-blind clinical trial, and the 40 patients were assigned into rose oil and placebo groups (n=20 per group). All patients were instructed to use their prescribed two soft capsules three times daily for two months. The clinical symptoms, quality of life the patients, and calprotectin level were evaluated via partial Mayo clinic score, irritable bowel disease questionnaire (IBDQ-9), and calprotectin kit as primary outcome measures. RESULTS: The mean age of the participants was 41±10 years. Most of them (53.6%) were male, and the remaining (46.4%) were female. The demographic and baseline data showed no differences between the two groups. Partial Mayo clinic scores decreased in both groups after the treatment, but the difference between the rose oil and placebo groups was not statistically significant (P=0.99). IBDQ-9 score also increased in both interventions before and after the treatment (P=0.012), though the differences between these two groups were not statistically significant (P=0.61). There were no significant differences between the two study groups either in terms of calprotectin level (P=0.219). CONCLUSION: This study showed that rose oil might improve ulcerative colitis clinical outcomes, but for a better evaluation, it is imperative to conduct experiments with a large sample size and longer follow-up observation.

Effect of selenium on testicular damage induced by varicocele in adult male Wistar rats.

PROJECT: Varicocele is an abnormal tortuosity and distension of the veins of the pampiniform plexus in the spermatic cord. It is the most common surgically correctable cause of male infertility. Several studies have revealed the effects of increased oxidative stress on serum, semen, and testicular tissues in patients with varicocele or in animal models. The aim of this study was to investigate the effects of sodium selenite on testicular damage induced by experimental left varicocele in male Wistar rats. PROCEDURE: In the present study, the effects of oral administration of sodium selenite (at doses of 0.05, 0.1, 0.2, and 0.4mg/kg bw) were assessed in normal and varicocelized rats. RESULTS: The varicocelized control rats showed decrease in sperm quality parameters, decreased activity of testes CAT, GPX and SOD, increased levels of MDA, and damage in testicular architecture. Administration of sodium selenite significantly reduced these changes to nearly normal levels, but did not change these parameters in normal rats. Histopathological studies further confirmed the protective effects of sodium selenite on varicocele-induced testicular damage in rats. Administrations of sodium selenite did not change these parameters in normal rats. CONCLUSIONS: Taken together, the results of this study suggest that sodium selenite treatment may have beneficial effect on the testes of varicocelized rats.