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In this paper, based on the Akaike information criterion, root mean square error and robustness coefficient, a rational evaluation of various epidemic models/methods, including seven empirical functions, four statistical inference methods and five dynamical models, on their forecasting abilities is carried out. With respect to the outbreak data of COVID-19 epidemics in China, we find that before the inflection point, all models fail to make a reliable prediction. The Logistic function consistently underestimates the final epidemic size, while the Gompertz's function makes an overestimation in all cases. Towards statistical inference methods, the methods of sequential Bayesian and time-dependent reproduction number are more accurate at the late stage of an epidemic. And the transition-like behavior of exponential growth method from underestimation to overestimation with respect to the inflection point might be useful for constructing a more reliable forecast. Compared to ODE-based SIR, SEIR and SEIR-AHQ models, the SEIR-QD and SEIR-PO models generally show a better performance on studying the COVID-19 epidemics, whose success we believe could be attributed to a proper trade-off between model complexity and fitting accuracy. Our findings not only are crucial for the forecast of COVID-19 epidemics, but also may apply to other infectious diseases., 25 pages, 5 figures, 2 tables

In respect of fire resistance and fire integrity, the charring rate is the most important property of timber. It has been a worldwide research focus to develop a charring model for predicting the charring rate. The objective of this study is to establish an integral charring model, which is based on a tailored thermodynamic equation for commercial Chinese timber species. At 50 kW/m2 heat flux, results show that the cone calorimeter can equal the furnace trials for testing the charring rate and also establish a charring rate model with a relative error of less than 20%. The integral model at a heat flux of 50 kW/m2 is safer to predict the charring rate than the other two models.

The dynamics of p53 play important roles in the regulation of cell fate decisions in response to various stresses, and programmed cell death 5 (PDCD5) functions as a co-activator of p53 that modulates p53 dynamics. In the present paper, we investigated how p53 dynamics are modulated by PDCD5 during the deoxyribose nucleic acid damage response using methods of bifurcation analysis and potential landscape. Our results revealed that p53 activities display rich dynamics under different PDCD5 levels, including monostability, bistability with two stable steady states, oscillations, and the coexistence of a stable steady state (or two states) and an oscillatory state. The physical properties of the p53 oscillations were further demonstrated by the potential landscape in which the potential force attracts the system state to the limit cycle attractor, and the curl flux force drives coherent oscillation along the cyclic trajectory. We also investigated the efficiency with which PDCD5 induced p53 oscillations. We show that Hopf bifurcation can be induced by increasing the PDCD5 efficiency and that the system dynamics exhibited clear transition features in both barrier height and energy dissipation when the efficiency was close to the bifurcation point.

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The tumor suppressor p53 plays a central role in cell fate decisions after DNA damage. Programmed Cell Death 5 (PDCD5) interacts with the p53 pathway to promote cell apoptosis. Recombinant human PDCD5 can significantly sensitize different cancers to chemotherapies. In the present paper, we construct a computational model that includes PDCD5 interactions in the p53 signaling network and study the effects of PDCD5 on p53-mediated cell fate decisions during the DNA damage response. Our results revealed that PDCD5 functions as a co-activator of p53 and regulates p53-dependent cell fate decisions via the mediation of p53 dynamics. The effects of PDCD5 are dose-dependent, such that p53 activity exhibits sustained low level, pulsed oscillations, or sustained high level dynamics depending on the PDCD5 level following DNA damage. Moreover, PDCD5 regulates caspase-3 activation via two mechanisms during the two phases of sustained and pulsed p53 dynamics. This study provides insights regarding how PDCD5 functions as a regulator of the p53 pathway and might be helpful for increasing our understanding of the molecular mechanisms by which PDCD5 can be used to treat cancers.

National audience

This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems., 17 pages

This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\leq 0$ such that the solution is positive for all time $t>0$. The condition is "optimal". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\omega$ limit set of this dynamical system, which can provide informations about the long time behavior of positive solutions of the delay differential equation., Comment: 15 pages, 2 figures

We have used a mathematical model of the combined dynamics of the hematopoietic stem cells and the differentiated neutrophil progeny to examine the effects of periodic chemotherapy in generating neutropenia, and the corresponding response of this system to granulocyte colony stimulating factor given to counteract the neutropenia. We find that there is a significant period of chemotherapy delivery that induces resonance in the system (at a period twice the average neutrophil lifespan from commitment to death) and a corresponding neutropenia suggesting that myelosuppressive protocols should avoid this period to minimize hematopoietic damage. The response to G-CSF is highly variable.

Programmed cell death 5 (PDCD5) is a human apoptosis-related molecule that is involved in both the cytoplasmic caspase-3 activity pathway (by regulating Bax translocation from cytoplasm to mitochondria) and the nuclear pathway (by interacting with Tip60). In this study, we developed a mathematical model of the PDCD5-regulated switching of the cell response from DNA repair to apoptosis after ultraviolet irradiation-induced DNA damage. We established the model by combining several hypotheses with experimental observations. Our simulations indicate that the ultimate cell response to DNA damage is dependent on a signal threshold mechanism, and the PDCD5 promotion of Bax translocation plays an essential role in PDCD5-regulated cell apoptosis. Furthermore, the model simulations revealed that PDCD5 nuclear translocation can attenuate cell apoptosis, and PDCD5 interactions with Tip60 can accelerate DNA damage-induced apoptosis, but the final cell fate decision is insensitive to the PDCD5-Tip60 interaction. These results are consistent with experimental observations. The effect of recombinant human PDCD5 was also investigated and shown to sensitize cells to DNA damage by promoting caspase-3 activity.