Inefficiency of SIR models in forecasting COVID-19 epidemic: a case study of Isfahan.

The multifaceted destructions caused by COVID-19 have been compared to that of World War II. What makes the situation even more complicated is the ambiguity about the duration and ultimate spread of the pandemic. It is especially critical for the governments, healthcare systems, and economic sectors to have an estimate of the future of this disaster. By using different mathematical approaches, including the classical susceptible-infected-recovered (SIR) model and its derivatives, many investigators have tried to predict the outbreak of COVID-19. In this study, we simulated the epidemic in Isfahan province of Iran for the period from Feb 14th to April 11th and also forecasted the remaining course with three scenarios that differed in terms of the stringency level of social distancing. Despite the prediction of disease course in short-term intervals, the constructed SIR model was unable to forecast the actual spread and pattern of epidemic in the long term. Remarkably, most of the published SIR models developed to predict COVID-19 for other communities, suffered from the same inconformity. The SIR models are based on assumptions that seem not to be true in the case of the COVID-19 epidemic. Hence, more sophisticated modeling strategies and detailed knowledge of the biomedical and epidemiological aspects of the disease are needed to forecast the pandemic.

Bifurcation analysis of a modular model of embryonic kidney development.

Many biological processes show switching behaviors in response to parameter changes. Although numerous surveys have been conducted on bifurcations in biological systems, they commonly focus on over-represented parts of signaling cascades, known as motifs, ignoring the multi-motif structure of biological systems and the communication links between these building blocks. In this paper, a method is proposed which partitions molecular interactions to modules based on a control theory point of view. The modules are defined so that downstream effect of one module is a regulator for its neighboring modules. Communication links between these modules are then considered as bifurcation parameters to reveal change in steady state status of each module. As a case-study, we generated a molecular interaction map of signaling molecules during the development of mammalian embryonic kidneys. The whole system was divided to modules, where each module is defined as a group of interacting molecules that result in expression of a vital downstream regulator. Bifurcation analysis was then performed on these modules by considering the communication signals as bifurcation parameters. Two-parameter bifurcation analysis was then performed to assess the effects of simultaneous input signals on each module behavior. In the case where a module had more than two inputs, a series of two parameter bifurcation diagrams were calculated each corresponding to different values of the third parameter. We detected multi-stability for RET protein as a key regulator for fate determination. This finding is in agreement with experimental data indicating that ureteric bud cells are bi-potential, able to form tip or trunk of the bud based on their RET activity level. Our findings also indicate that Glial cell-derived neurotrophic factor (GDNF), a known potent regulator of kidney development, exerts its fate-determination function on cell placement through destruction of saddle node bifurcation points in RET steady states and confining RET activity level to high activity in ureteric bud tip. In conclusion, embryonic cells usually show a huge decision making potential; the proposed modular modeling of the system in association with bifurcation analysis provides a quantitative holistic view of organ development.

Agent-based modeling and bifurcation analysis reveal mechanisms of macrophage polarization and phenotype pattern distribution.

Macrophages play a key role in tissue regeneration by polarizing to different destinies and generating various phenotypes. Recognizing the underlying mechanisms is critical in designing therapeutic procedures targeting macrophage fate determination. Here, to investigate the macrophage polarization, a nonlinear mathematical model is proposed in which the effect of IL4, IFNγ and LPS, as external stimuli, on STAT1, STAT6, and NFκB is studied using bifurcation analysis. The existence of saddle-node bifurcations in these internal key regulators allows different combinations of steady state levels which are attributable to different fates. Therefore, we propose dynamic bifurcation as a crucial built-in mechanism of macrophage polarization. Next, in order to investigate the polarization of a population of macrophages, bifurcation analysis is employed aligned with agent-based approach and a two-layer model is proposed in which the information from single cells is exploited to model the behavior in tissue level. Also, in this model, a partial differential equation describes the diffusion of secreted cytokines in the medium. Finally, the model was validated against a set of experimental data. Taken together, we have here developed a cell and tissue level model of macrophage polarization behavior which can be used for designing therapeutic interventions.

Analysis of time-course microarray data: Comparison of common tools.

High-throughput time-series data have a special value for studying the dynamism of biological systems. However, the interpretation of such complex data can be challenging. The aim of this study was to compare common algorithms recently developed for the detection of differentially expressed genes in time-course microarray data. Using different measures such as sensitivity, specificity, predictive values, and related signaling pathways, we found that limma, timecourse, and gprege have reasonably good performance for the analysis of datasets in which only test group is followed over time. However, limma has the additional advantage of being able to report significance cut off, making it a more practical tool. In addition, limma and TTCA can be satisfactorily used for datasets with time-series data for all experimental groups. These findings may assist investigators to select appropriate tools for the detection of differentially expressed genes as an initial step in the interpretation of time-course big data.

Colored petri net modeling of small interfering RNA-mediated messenger RNA degradation.

BACKGROUND: Mathematical modeling of biological systems is an attractive way for studying complex biological systems and their behaviors. Petri Nets, due to their ability to model systems with various levels of qualitative information, have been wildly used in modeling biological systems in which enough qualitative data may not be at disposal. These nets have been used to answer questions regarding the dynamics of different cell behaviors including the translation process. In one stage of the translation process, the RNA sequence may be degraded. In the process of degradation of RNA sequence, small-noncoding RNA molecules known as small interfering RNA (siRNA) match the target RNA sequence. As a result of this matching, the target RNA sequence is destroyed. MATERIALS AND METHODS: In this context, the process of matching and destruction is modeled using Colored Petri Nets (CPNs). The model is constructed using CPNs which allow tokens to have a value or type on them. Thus, CPN is a suitable tool to model string structures in which each element of the string has a different type. Using CPNs, long RNA, and siRNA strings are modeled with a finite set of colors. The model is simulated via CPN Tools. RESULTS: A CPN model of the matching between RNA and siRNA strings is constructed in CPN Tools environment. CONCLUSION: In previous studies, a network of stoichiometric equations was modeled. However, in this particular study, we modeled the mechanism behind the silencing process. Modeling this kind of mechanisms provides us with a tool to examine the effects of different factors such as mutation or drugs on the process.