Application of conditional robust calibration to ordinary differential equations models in computational systems biology: a comparison of two sampling strategies

Bayesian parameter estimation for dynamical models in systems biology

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and '-omics' studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experimental measurements, lack of detailed molecular mechanisms underlying the reactions, and missing biochemical interactions. Additionally, the inherent nonlinearities with respect to the states and parameters associated with the system of differential equations further compound the challenges of parameter estimation. In this study, we propose a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We apply these methods to a series of signaling models of increasing mathematical complexity. Systematic analysis of these dynamical systems showed that parameter estimation depends on data sparsity, noise level, and model structure, including the existence of multiple steady states. These results highlight how focused uncertainty quantification can enrich systems biology modeling and enable additional quantitative analyses for parameter estimation.

Robustness analysis for quantitative assessment of vaccination effects and SARS-CoV-2 lineages in Italy

Background

In Italy, the beginning of 2021 was characterized by the emergence of new variants of SARS-CoV-2 and by the availability of effective vaccines that contributed to the mitigation of non-pharmaceutical interventions and to the avoidance of hospital collapse.

Methods

We analyzed the COVID-19 propagation in Italy starting from September 2021 with a Susceptible-Exposed-Infected-Recovered (SEIR) model that takes into account SARS-CoV-2 lineages, intervention measures and efficacious vaccines. The model was calibrated with the Bayesian method Conditional Robust Calibration (CRC) using COVID-19 data from September 2020 to May 2021. Here, we apply the Conditional Robustness Analysis (CRA) algorithm to the calibrated model in order to identify model parameters that most affect the epidemic diffusion in the long-term scenario. We focus our attention on vaccination and intervention parameters, which are the key parameters for long-term solutions for epidemic control.

Results

Our model successfully describes the presence of new variants and the impact of vaccinations and non-pharmaceutical interventions in the Italian scenario. The CRA analysis reveals that vaccine efficacy and waning immunity play a crucial role for pandemic control, together with asymptomatic transmission. Moreover, even though the presence of variants may impair vaccine effectiveness, virus transmission can be kept low with a constant vaccination rate and low restriction levels.

Conclusions

In the long term, a policy of booster vaccinations together with contact tracing and testing will be key strategies for the containment of SARS-CoV-2 spread.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12879-022-07395-2.

A Modeling Study on Vaccination and Spread of SARS-CoV-2 Variants in Italy

From the end of 2020, different vaccines against COVID-19 have been approved, offering a glimmer of hope and relief worldwide. However, in late 2020, new cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) started to re-surge, worsened by the emergence of highly infectious variants. To study this scenario, we extend the Susceptible-Exposed-Infectious-Removed model with lockdown measures used in our previous work with the inclusion of new lineages and mass vaccination campaign. We estimate model parameters using the Bayesian method Conditional Robust Calibration in two case studies: Italy and the Umbria region, the Italian region being worse affected by the emergence of variants. We then use the model to explore the dynamics of COVID-19, given different vaccination paces and a policy of gradual reopening. Our findings confirm the higher reproduction number of Umbria and the increase of transmission parameters due to the presence of new variants. The results illustrate the importance of preserving population-wide interventions, especially during the beginning of vaccination. Finally, under the hypothesis of waning immunity, the predictions show that a seasonal vaccination with a constant rate would probably be necessary to control the epidemic.

Application of Response Surface Methodology for Optimizing the Therapeutic Activity of ZnO Nanoparticles Biosynthesized from Aspergillus niger

In this study, the biosynthesis of zinc oxide nanoparticles using Aspergillus niger (A/ZnO-NPs) is described. These particles have been characterized by UV-Vis spectrum analysis, X-ray powder diffraction, field emission scanning electron microscopy, and transmission electron microscopy. To use this biosynthesized nanoparticle as an antiproliferative and antimicrobial agent, the IC₅₀ value against the breast cancer cell line and inhibition zone against Escherichia coli were used to optimize the effect of two processing factors including dose of filtrate fungi cell and temperature. The biosynthesized A/ZnO-NPs had an absorbance band at 320 nm and spherical shapes. The mean particles size was 35 nm. RSM (response surface methodology) was utilized to investigate the outcome responses. The Model F-value of 12.21 and 7.29 implies that the model was significant for both responses. The contour plot against inhibition zone for temperature and dose showed that if the dose increases from 3.8 to 17.2 µg/mL, the inhibition zone increases up to 35 mm. As an alternative to chemical and/or physical methods, biosynthesizing zinc oxide NPs through fungi extracts can serve as a more facile and eco-friendly strategy. Additionally, for optimization of the processes, the outcome responses in the biomedical available test can be used in the synthesis of ZnO-NPs that are utilized for large-scale production in various medical applications.

Mathematical Modeling and Robustness Analysis to Unravel COVID-19 Transmission Dynamics: The Italy Case

This study started from the request of providing predictions on hospitalization and Intensive Care Unit (ICU) rates that are caused by COVID-19 for the Umbria region in Italy. To this purpose, we propose the application of a computational framework to a SEIR-type (Susceptible, Exposed, Infected, Removed) epidemiological model describing the different stages of COVID-19 infection. The model discriminates between asymptomatic and symptomatic cases and it takes into account possible intervention measures in order to reduce the probability of transmission. As case studies, we analyze not only the epidemic situation in Umbria but also in Italy, in order to capture the evolution of the pandemic at a national level. First of all, we estimate model parameters through a Bayesian calibration method, called Conditional Robust Calibration (CRC), while using the official COVID-19 data of the Italian Civil Protection. Subsequently, Conditional Robustness Analysis (CRA) on the calibrated model is carried out in order to quantify the influence of epidemiological and intervention parameters on the hospitalization rates. The proposed pipeline properly describes the COVID-19 spread during the lock-down phase. It also reveals the underestimation of new positive cases and the need of promptly isolating asymptomatic and presymptomatic cases. The results emphasize the importance of the lock-down timeliness and provide accurate predictions on the current evolution of the pandemic.