Mathematics

Covid-19 is characterized by rapid transmission and severe symptoms, leading to deaths in some cases (ranging from 1.5 to 12% of the affected, depending on the country). We identify the Gaussian nature of mortality due to covid-19, as shown in China where it appears to have run its course (during the first sweep of the pandemic at least) and other coutnries, and also in Imperial College modeling. Gaussian distribution involves three parameters, the height, peak location and the width, and the streaming data can be used to infer function value, slope and inflection location as a minimum set of constraints to estimate the subsequent trajectories. Thus, we apply the Gaussian function template as the basis for a data-assimilated model of covid-19 trajectories, first to USA, United Kingdom (UK), Iran and the world total in this study. As more data become available, the Gaussian trajectories are updated, for other nations and also for state-by-state projections in USA.

The outbreak of COVID-19 has an undeniable global impact, both socially and economically. March 11th, 2020, COVID-19 was declared as a pandemic worldwide. Many governments, worldwide, have imposed strict lockdown measures to minimize the spread of COVID-19. However, these measures cannot last forever; therefore, many countries are already considering relaxing the lockdown measures. This study, quantitatively, investigated the impact of this relaxation in the United States, Germany, the United Kingdom, Italy, Spain, and Canada. A modified version of the SIR model is used to model the reduction in lockdown based on the already available data. The results showed an inevitable second wave of COVID-19 infection following loosening the current measures. The study tries to reveal the predicted number of infected cases for different reopening dates. Additionally, the predicted number of infected cases for different reopening dates is reported.

We consider a simple model for the COVID-19 pandemic to analyse the relative effectiveness of several stages of the lockdown in Belgium, as well as of several phases of its relaxation. We also make a future projection of different types of measures relative to different stages of the already experienced lockdown.

Using a modified form of the SIR model, we show that, under general conditions, all pandemics exhibit certain scaling rules. Using only daily data for symptomatic, confirmed cases, these scaling rules can be used to estimate: (i) reff, the effective pandemic R-parameter; (ii) ftot, the fraction of exposed individuals that were infected (symptomatic and asymptomatic); (iii) Leff, the effective latency, the average number of days an infected individual is able to infect others in the pool of susceptible individuals; and (iv) , the probability of infection per contact between infected and susceptible individuals. We validate the scaling rules using an example and then apply our method to estimate reff, ftot, Leff and for the first phase of the SARS-Cov-2, Covid-19 pandemic for several countries where there was a well separated first peak in identified infected daily cases after the outbreak of the pandemic in early 2020. Our results are general and can be applied to any pandemic.

We know that SARS-Cov2 produces the new COVID-19 disease, which is one of the most dangerous pandemics of modern times. This pandemic has critical health and economic consequences, and even the health services of the large, powerful nations may be saturated. Thus, forecasting the number of infected persons in any country is essential for controlling the situation. In the literature, different forecasting methods have been published, attempting to solve the problem. However, a simple and accurate forecasting method is required for its implementation in any part of the world. This paper presents a precise and straightforward forecasting method named SVR-ESAR (Support Vector regression hybridized with the classical Exponential smoothing and ARIMA). We applied this method to the infected time series in four scenarios, which we have taken for the Github repository: the Whole World, China, the US, and Mexico. We compared our results with those of the literature showing the proposed method has the best accuracy.

Predictions of the COVID-19 pandemic in USA are compared using curve fitting and various recurrent neural networks (RNNs) including the standard long short-term memory (LSTM) RNN and 10 types of slim LSTM RNNs. The curve fitting method predicts the pandemic would end in early summer but the exact date and scale vary with the evolving data used for fitting. All LSTM RNNs result in short-term (8 to 10 days) predictions with comparable accuracies (smaller than 10 %) to curve fitting--they do not show advantage over curve fitting.

A model for the joint motion of the basilar membrane (BM) and the outer hair cells (OHC) in the cochlea is presented. The model consists of two one-dimensional mass distributions, one along the OHC and outer hair bundle (OHB) interface, and one along the BM. The motion of these masses is driven by the forces exerted on them by the elastic bodies connecting them and by the pressure difference in the fluids separated by the BM. The model includes a nonlinear motility of the OHC and its coupling with the vibrations of the BM. The model implies a Hopf bifurcation for the dynamical system governing the two coupled distributed oscillators. It is shown that when the system operates near the bifurcation point the BM motion is amplified up to a saturation level. The model provides very sharp frequency decomposition of the incident audio signal according to the place principle. It also acts as a powerful filter that distinguishes pure tones even in the presence of louder noisy background. In addition to simulations of the model, the unusual role played by the OHC friction is studied. Energy estimates are derived for the model functions.

In the present work, we propose a new integrated mathematical model for the neuromuscular activation of a motor unit, describing the four consecutive processes, leading to muscle contraction--neural impulse propagation, acetylcholine transport in the neuromuscular junction, calcium release in the muscle cell, and force generation. We connect in an appropriate way models of the respective processes, known from the literature, and validate the resulting model by showing that it can reproduce with high accuracy experimental data for two motor unit twitches on a rat medial gastrocnemius muscle and can numerically restore the sequence of events that result in force generation. Sensitivity analysis for some of the model parameters is further performed to study their effect on the model solutions and to show that they can be related to known malfunctions or treatments of the neuromuscular system.

Homeostasis is kind of force that makes living organism to live. In this study, we suggest an integral equation that models homeostasis in living organism. We also showed that various situations can be modeled by homeostasis, and give mathematical interpretation of mechanism of living organism. With our proposed integral equation, one can handle homeostasis quantitatively, and this approach is expected to unveil various hidden properties of living organism.

For a given running speed and for any wind speed, we calculate the slope for which the effort to overcome in the absence of wind is energetically equivalent to running with the original wind speed on a flat track. The influence of headwind and tailwind is thus made numerically comparable to the influence of a positive or negative slope. The same applies to the lack of air resistance on a treadmill and its compensation by adjusting the incline. Moreover, for turning point routes physiological corrections are considered and the impact of speed adjustments is analyzed.

The refractory period of cardiac tissue can be quantitatively described using strength-interval (SI) curves. The information captured in SI curves is pertinent to the design of anti-arrhythmic devices including pacemakers and implantable cardioverter defibrillators. As computational cardiac modelling becomes more prevalent, it is feasible to consider the generation of computationally derived SI curves as a supplement or precursor to curves that are experimentally derived. It is beneficial, therefore, to examine the profiles of the SI curves produced by different cardiac tissue models to determine whether some models capture the refractory period more accurately than others. In this study, we compare the unipolar SI curves of two tissue models: the current state-of-the-art bidomain model and the recently developed extracellular-membrane-intracellular (EMI) model. The EMI models resolution of individual cell structure makes it a more detailed model than the bidomain model, which forgoes the structure of individual cardiac cells in favour of treating them homogeneously as a continuum. We find that the resulting SI curves elucidate differences between the models, including that the behaviour of the EMI model is noticeably closer to the refractory behaviour of experimental data compared to that of the bidomain model. These results hold implications for future computational pacemaker simulations and shed light on the predicted refractory properties of cardiac tissue from each model. Author summaryMathematical modelling and computational simulation of cardiac activity have the potential to greatly enhance our understanding of heart function and improve the precision of cardiac medicine. The current state-of-the-art model is the bidomain model, which considers a volume average of cardiac activity. Although the bidomain model has had success in several applications, in other situations, its approach may obscure critical details of heart function. The extracellular-membrane-intracellular (EMI) model is a recently developed model of cardiac tissue that addresses this limitation. It models cardiac cells individually; therefore, it offers significantly greater physiological accuracy than bidomain simulations. This increase in accuracy comes at a higher computational cost, however. To explore the benefits of one model over the other, here we compare the performance of the bidomain and EMI models in a pacing study of cardiac tissue often employed in pacemaker design. We find that the behaviour of the EMI model is noticeably closer to experimental data than the behaviour of the bidomain model. These results hold implications for future pacemaker design and improve our understanding of the two models in relation to one another.

The article presents a novel stochastic mathematical model of mitosis in heterogeneous (multiple-phenotype), age-dependent cell populations. The developed computational techniques involve flexible use of differentiation tree diagrams. The applicability of the model is discussed in the context of the Haeckelian (biogenetic) paradigm. In particular, the article puts forward the conjecture of generality of Haeckels recapitulation law. The conjecture is briefly collated against relevant scientific evidence and elaborated for the specific case of evolving/mutable cell phenotypes as considered by the model. The feasibility, basic regimes and the convenience of the model are tested on examples and experimental data, and the corresponding open source simulation software is described and demonstrated.

Following the suggestion of L. F. Jaffe [1] we propose a mathematical model of fast calcium induced calcium influx waves (CICI Waves). They can propagate at relatively high speeds (up to 1300 micrometers/s). According to [1], they propagate due to a mechanochemical interaction of actomyosin network with the cell membrane. The local stretching of the membrane caused by actin filaments opens mechanically operated ion channels resulting in the influx of calcium to the cell. Moreover, stretching a cells membrane at one point opens nearby stretch activated calcium channels because the mechanical force is relayed by the actin filaments interconnected by myosin bridges. The number of bridges as well as filament density increases with calcium concentration, causing the contraction of the actomyosin network. Thus, the force acting on the membrane from tangled actin filaments is transmitted ahead of the moving front of the calcium concentration. As a result, the ion channels are opened even before the signal of calcium reaches them. This leads to much larger propagation speed of CICI waves in comparison with calcium induced calcium released (CICR) waves, where the wave is sustained by the diffusion of calcium and autocatalytic release of calcium from the internal stores (e.g. endoplasmic reticula).

Model tuning with the optimization of pipeline configuration is a well-established practice for the development of machine learning models. However, this often entails an exhaustive search process, especially as the parameter space expands with increasing model complexity. In the emerging field of quantum machine learning (QML), there is limited literature on the effects of configuration parameters, especially quantum-specific ones, and their choices on model performance. To address this gap, here we present a study exploring the impacts of data scaling and configuration parameters in quantum neural network (QNN) development using beta regression. Our experiments with two benchmark datasets showed that a well-tuned QNN can achieve predictive performance comparable to its classical counterparts. Our findings also demonstrate useful reference points of QNN model tuning to support a more efficient parameter optimization process.

BackgroundExponential-like infection growths leading to peaks (which could be the inflection points or turning points) are usually the hallmarks of infectious disease outbreaks including coronaviruses. To predict the inflection points, i.e., inflection time (Tmax) & maximal infection number (Imax) of the novel coronavirus (COVID-19), we adopted a trial and error strategy and explored a series of approaches from simple logistic modeling (that has an asymptomatic line) to sophisticated tipping point detection techniques for detecting phase transitions but failed to obtain satisfactory results. MethodInspired by its success in diversity-time relationship (DTR), we apply the PLEC (power law with exponential cutoff) model for detecting the inflection points of COVID-19 outbreaks. The model was previously used to extend the classic species-time relationship (STR) for general DTR (Ma 2018), and it has two "secondary" parameters (computed from its 3 parameters including power law scaling parameter w, taper-off parameter d to overwhelm virtually exponential growth ultimately, and a parameter c related to initial infections): one that was originally used for estimating the potential or dark biodiversity is proposed to estimate the maximal infection number (Imax) and another is proposed to determine the corresponding inflection time point (Tmax). ResultsWe successfully estimated the inflection points [Imax, Tmax] for most provinces ({approx}85%) in China with error rates <5% in both Imax and Tmax. We also discussed the constraints and limitations of the proposed approach, including (i) sensitive to disruptive jumps, (ii) requiring sufficiently long datasets, and (iii) limited to unimodal outbreaks.

Antimicrobial resistance (AMR) is a serious threat to global health today. The spread of AMR, along with the lack of new drug classes in the antibiotic pipeline, has resulted in a renewed interest in phage therapy, which is the use of bacteriophages to treat pathogenic bacterial infections. This therapy, which was successfully used to treat a variety of infections in the early twentieth century, had been largely dismissed due to the discovery of easy to use antibiotics. However, the continuing emergence of antibiotic resistance has motivated new interest in the use of phage therapy to treat bacterial infections. Though various models have been developed to address the AMR-related issues, there are very few studies that consider the effect of phage-antibiotic combination therapy. Moreover, some of biological details such as the effect of the immune system on phage have been neglected. To address these limitations, we utilized a mathematical model to examine the role of the immune response in concert with phage-antibiotic combination therapy compounded with the effects of the immune system on the phages being used for treatment. We explore the effect of phage-antibiotic combination therapy by adjusting the phage and antibiotics dose or altering the timing. The model results show that it is important to consider the host immune system in the model and that frequency and dose of treatment are important considerations for the effectiveness of treatment. Our study can lead to development of optimal antibiotic use and further reduce the health risks of the human-animal-plant-ecosystem interface caused by AMR.

Thermoregulation is crucial to homeostasis, but the mechanisms of its dysfunction are still largely mysterious, including fever, which is generally the most disconcerting sign of a serious infection or disease. Theories on body temperature dynamics that aim to explain a fever, such as changes in an internal setpoint, have been proposed, but none can identify the fundamental molecular pathways that produce a fever. Here, potential molecular pathways resultant in fever are identified, modeled, and compared to experimental temperature response data. Based on recent developments made by this lab, which has shown that the pyrogen prostaglandin E2 (PGE2) possesses similar binding affinity as the hormone cortisol (CORT) at the critical ligand binding domain (LBD) of glucocorticoid receptors (GR); molecular modeling, mathematical modeling and a case study for validation is used to indicate that competitive inhibition of CORT by PGE2 as a fundamental reason for dysfunctional dynamics of body temperature, including fever. Comprised of a superposition of proportional and derivative terms of signals representing temperature receptors, CORT concentration, and PGE2 concentration, the internal temperature control model characterizes dynamics associated with the cardiovascular, immune, and neural systems in response to infectious agents, triggering events, and other causal factors. The model is validated by examination of the transient and spectral characteristics of a three-day case history involving temperature trajectories after physical activity protocols in response to a standard vaccination of pneumococcal and influenza species.

Forecast of the peak-out and settling timing of COVID-19 at an early stage should help the people how to cope with the situation. Curve-fitting method with an asymmetric log-normal function has been applied to daily confirmed cases data in various countries. Most of the curve-fitting could show good forecasts, while the reason has not been clearly shown. The K value has recently been proposed which can provide good reasoning of curve-fitting mechanism by corresponding a long and steep slope on the K curve with fitting stability. Since K can be expressed by a time differential of logarithmic total cases, the physical background of the above correspondence was discussed in terms of the growth rate in epidemic entropy.

A discrete dynamic model for human epidemics was developed in present study. The model included major parameters as transmission strength and its decline parameters, mean incubation period, hospitalization time, non-hospitalization daily mortality, non-hospitalization daily recovery rate, and hospitalization proportion, etc. Sensitivity analysis of the model indicated the total cumulative cases significantly increased with initial transmission strength, hospitalization time. The total cumulative cases significantly decreased with transmission strengths decline and hospitalization proportion, and linearly decreased with non-hospitalization daily mortality and non-hospitalization daily recovery rate. In a certain range, the total cumulative cases significantly increased with mean incubation period. Sensitivity analysis demonstrated that dynamic change of transmission strength is one of the most important and controllable factors. In addition, reducing the delay for hospitalization is much effective in weakening disease epidemic. Non-hospitalization recovery rate is of importance for enhancing immunity to recover from the disease.

Nonlinear feedback controllers are ubiquitous features of biological systems at different scales. A key motif arising in these systems is a sequestration-based feedback. As a physiological example of this type of feedback architecture, platelets (specialized cells involved in blood clotting) differentiate from stem cells, and this process is activated by a protein called Thrombopoietin (TPO). Platelets actively sequester and degrade TPO, creating negative feedback whereby any depletion of platelets increases the levels of freely available TPO that upregulates platelet production. We show similar examples of sequestration-based feedback in intracellular biomolecular circuits involved in heat-shock response and microRNA regulation. Our systematic analysis of this feedback motif reveals that platelets induced degradation of TPO is critical in enhancing system robustness to external disturbances. In contrast, reversible sequestration of TPO without degradation results in poor robustness to disturbances. We develop exact analytical results quantifying the limits to which the sensitivity to disturbances can be attenuated by sequestration-based feedback. Next, we consider the stochastic formulation of the circuit that takes into account low-copy number fluctuations in feedback components. Interestingly, our results show that the extent of random fluctuations are enhanced with increasing feedback strength, but can exhibit local maxima and minima across parameter regimes. In summary, our systematic analysis highlights design principles for enhancing the robustness of sequestration-based feedback mechanisms to external disturbances and inherent noise in molecular counts.