We consider the flow of blood, treated as an incompressible Newtonian fluid, through vessels undergoing periodic oscillations. As remarked by many authors, in the absence of valves oscillations hinder the flow because of the lumen reduction. The underlying biological mechanism is the so-called vasomotion, observed long ago in small blood vessels. Here, we study the vasomotion in arterioles and provide its theoretical justification by analyzing the effect when the network of vessels downstream of the arterioles is considered. We thus explain both quantitatively and qualitatively, why the oscillations of the arteriole walls, a phenomenon that undoubtedly reduces blood flow at the level of the single arteriole, play a fundamental role in microcirculation. In "large" arterioles we analyze also the coupling between the vasomotion and the Fåhræus-Lindqvist effect (the tendency of the erythrocytes to accumulate towards the center). In particular, we prove that the presence of a cell depleted layer close to the vessel walls mitigates the disadvantage caused by the lumen reduction.

A heart attack, or acute myocardial infarction (MI) is caused by the acute occlusion of a coronary artery. MI is associated with 30% mortality; approximately half of the deaths occur prior to arrival at the hospital. Reperfusion therapy in the hospital is a medical treatment to restore blood flow through the blocked artery; treatment includes drugs and surgery. However, the damage to the heart muscles through the infarct area is permanent and there is additional damage around the infarct area due to inflammation or insufficient oxygen supply. Approximately half of the patients who survive MI are hospitalized again within one year after reperfusion treatment. In this paper we develop a mathematical model of MI and use it to assess the efficacy of drugs used, post reperfusion, to reduce the damage caused by inflammation in a region of the left ventricular wall surrounding the infarct area. The mathematical model, represented by a system of partial differential equations. The model variables include myocytes, endothelial cells, neutrophils, macrophages, fibroblasts and cytokines that play a role in the interactions among these cells. The drugs used to in the model include IL-1, TNF-α and TGF-β inhibitors, and the delivery of VEGF. The model is based on mice data. In particular, we find that immunomodulatory treatment with TNF-α and IL-1 inhibitors can significantly increase the low density of myocytes bordering the infarct area by 50-60% and decrease the abnormally high density of ECM in a region surrounding the infarct area.

New emerging nano-scale technologies like hydrogenated noncrystalline-silicon thin-film transistors (TFTs) and memristors, fabricated at low temperatures and over large areas, permit low-cost processing and 3D integration with CMOS cores. Here, we aim to propose a mathematical model which explains the memory-TFT threshold voltage shift due to the gate bias instability. Then, based on this mathematical approach, we propose a novel learning synapse composed of a voltage/flux driven memristor in parallel with a common-source memory-TFT with a memristive load. The proposed device realizes the triplet-based spike-timing-dependent plasticity rule (TSTDP) as a more realistic form of learning than the purely pair-based STDP (PSTDP). PSTDP is a synaptic learning rule which utilizes a constant-frequency pairing protocol to induce synaptic weight change and cannot explain the modification due to the frequency changes of spike pairs, and also the outcomes of triplet and quadruplet experiments. However, TSTDP improves the learning capabilities of the conventional PSTDP and reproduces the results of more electrophysiological experiments. In this paper, we apply various spike patterns like different-frequency and different-timing spike pairs, spike triplets, and quadruplets to the proposed device. Our simulations confirm a close match with the experimental data sets of real biological synapses.

As a common infectious disease, scarlet fever has exposed a tendency of slow fluctuating ups and downs in recent years with a certain periodicity. In this work, a novel differential equation epidemic model with freely transmitted viruses is introduced to investigate the transmission dynamics of scarlet fever in Northwest China. First, the correlation analysis reveals that the incidence rate of scarlet fever is significantly positively correlated with air pressure (r = 0.61), conversely negatively correlated with precipitation (r = -0.15). Furthermore, the basic reproduction number R0 is derived, and this paper proves that the unique disease-free periodic solution P0 is globally symptotically stable when R0 < 1, while the disease is uniformly persistent and at least one positive periodic solution exists when R0 > 1. Moreover, by studying the qualitative of correlation between the effective reproduction number and air pollutants or meteorological factors, the seasonal variation pattern of incidence is summarized. Our investigations suggest that the relevant epidemic prevention departments should pay close attention to changes in environmental factors of the five provinces of Northwest China to formulate timely prevention strategies before the arrival of the high-risk period.

Measles, mumps and rubella (MMR) vaccine program was introduced in Jiangsu province of China in May 2008 and has been greatly contributed to decreasing of mumps cases. However, mumps has been resurging since May 2015. A number of studies have put forward that the resurgence of mumps is due to vaccine failure. In this paper, we investigated the other reasons for the resurging of mumps, such as the changes in seasonal transmission patterns and demographic structures, by using an age-structured mathematical model. We divided the history (January 2005 to May 2019) of mumps epidemics of Jiangsu province into three different stages: No vaccine stage (January 2005 to December 2008), effectively controlled stage (January 2009 to December 2014) and resurgence stage (January 2015 to May 2019). The features of mumps epidemics in three stages are compared under different demographic structures with same physical contact rate. The mumps transmission rate was increased in summer and dropped in November in stage III compared with that in stage I. The changes in demographic structures give a good explanation why the mumps outbreaked among children around 10 years old in stage I and around 5 years old in stage III. We have a conclusion that the vaccine failure, changes in seasonality and demographic structures were associated with the mumps outbreaks in recent years in Jiangsu province, China. We give the patterns of mumps dynamics considering age, vaccine, seasonality and demographic structures, which can help health program planners to implement more preventive interventions in mumps control during the period of higher risk of infection.

The many respiratory viruses that cause influenza-like illness (ILI) are reported and tracked as one entity, defined by the CDC as a group of symptoms that include a fever of 100 degrees Fahrenheit, a cough, and/or a sore throat. In the United States alone, ILI impacts 9-49 million people every year. While tracking ILI as a single clinical syndrome is informative in many respects, the underlying viruses differ in parameters and outbreak properties. Most existing models treat either a single respiratory virus or ILI as a whole. However, there is a need for models capable of comparing several individual viruses that cause respiratory illness, including ILI. To address this need, here we present a flexible model and simulations of epidemics for influenza, RSV, rhinovirus, seasonal coronavirus, adenovirus, and SARS/MERS, parameterized by a systematic literature review and accompanied by a global sensitivity analysis. We find that for these biological causes of ILI, their parameter values, timing, prevalence, and proportional contributions differ substantially. These results demonstrate that distinguishing the viruses that cause ILI will be an important aspect of future work on diagnostics, mitigation, modeling, and preparation for future pandemics.

New experimental data have shown how the periodic exposure of cells to low oxygen levels (i.e., cyclic hypoxia) impacts their progress through the cell-cycle. Cyclic hypoxia has been detected in tumours and linked to poor prognosis and treatment failure. While fluctuating oxygen environments can be reproduced in vitro, the range of oxygen cycles that can be tested is limited. By contrast, mathematical models can be used to predict the response to a wide range of cyclic dynamics. Accordingly, in this paper we develop a mechanistic model of the cell-cycle that can be combined with in vitro experiments to better understand the link between cyclic hypoxia and cell-cycle dysregulation. A distinguishing feature of our model is the inclusion of impaired DNA synthesis and cell-cycle arrest due to periodic exposure to severely low oxygen levels. Our model decomposes the cell population into five compartments and a time-dependent delay accounts for the variability in the duration of the S phase which increases in severe hypoxia due to reduced rates of DNA synthesis. We calibrate our model against experimental data and show that it recapitulates the observed cell-cycle dynamics. We use the calibrated model to investigate the response of cells to oxygen cycles not yet tested experimentally. When the re-oxygenation phase is sufficiently long, our model predicts that cyclic hypoxia simply slows cell proliferation since cells spend more time in the S phase. On the contrary, cycles with short periods of re-oxygenation are predicted to lead to inhibition of proliferation, with cells arresting from the cell-cycle in the G2 phase. While model predictions on short time scales (about a day) are fairly accurate (i.e, confidence intervals are small), the predictions become more uncertain over longer periods. Hence, we use our model to inform experimental design that can lead to improved model parameter estimates and validate model predictions.

Human immunodeficiency virus type-1 (HIV-1) attaches to target cells and releases the capsid, an essential component of the viral core that contains viral RNA, into the cytoplasm. After invading target cells, the core structure gradually collapses. The timing of the disassembly of the HIV-1 capsid is essential for efficient viral cDNA synthesis and transport into the nucleus. HIV-1 uncoating is controlled by the host factor maternal embryonic leucine zipper kinase (MELK); however, the quantitative and dynamic relationship between the HIV-1 uncoating process and HIV-1 infection remains unresolved. In this study, we quantified the uncoating process on HIV-1 cDNA synthesis and transport into the nucleus by combining a mathematical model with in vitro data. In addition, detailed in silico simulations demonstrated host factors, including MELK, optimize transport efficiency. Our experimental-mathematical approach revealed quantitative dynamics of the HIV-1 uncoating process, indicating that increasing the speed of uncoating always reduces the amount of HIV-1 cDNA in the nucleus.

Many SARS-CoV-2 variants have appeared over the last months, and many more will continue to appear. Understanding the competition between these different variants could help make future predictions on the evolution of epidemics. In this study we use a mathematical model to investigate the impact of three different SARS-CoV-2 variants on the spread of COVID-19 across France, between January-May 2021 (before vaccination was extended to the full population). To this end, we use the data from Geodes (produced by Public Health France) and a particle swarm optimisation algorithm, to estimate the model parameters and further calculate a value for the basic reproduction number R0. Sensitivity and uncertainty analysis is then used to better understand the impact of estimated parameter values on the number of infections leading to both symptomatic and asymptomatic individuals. The results confirmed that, as expected, the alpha, beta and gamma variants are more transmissible than the original viral strain. In addition, the sensitivity results showed that the beta/gamma variants could have lead to a larger number of infections in France (of both symptomatic and asymptomatic people).

Tumors consist of heterogeneous cell subpopulations that may develop differing phenotypes, such as increased cell growth, metastatic potential and treatment sensitivity or resistance. To study the dynamics of cancer development at a single-cell level, we model the tumor microenvironment as a metapopulation, in which habitat patches correspond to possible sites for cell subpopulations. Cancer cells may emigrate into dispersal pool (e.g. circulation system) and spread to new sites (i.e. metastatic disease). In the patches, cells divide and new variants may arise, possibly leading into an invasion provided the aberration promotes the cell growth. To study such adaptive landscape of cancer ecosystem, we consider various evolutionary strategies (phenotypes), such as emigration and angiogenesis, which are important determinants during early stages of tumor development. We use the metapopulation fitness of new variants to investigate how these strategies evolve through natural selection and disease progression. We further study various treatment effects and investigate how different therapy regimens affect the evolution of the cell populations. These aspects are relevant, for example, when examining the dynamic process of a benign tumor becoming cancerous, and what is the best treatment strategy during the early stages of cancer development. It is shown that positive angiogenesis promotes cancer cell growth in the absence of anti-angiogenic treatment, and that the anti-angiogenic treatment reduces the need of cytotoxic treatment when used in a combination. Interestingly, the model predicts that treatment resistance might become a favorable quality to cancer cells when the anti-angiogenic treatment is intensive enough. Thus, the optimal treatment dosage should remain below a patient-specific level to avoid treatment resistance.

The end-of-outbreak declaration is an important part of epidemic control, marking the relaxation or cancellation of prevention and control measures. We propose a probability model to retrospectively quantify the confidence of giving the end-of-outbreak declaration during the COVID-19 epidemic in early 2020 in Wuhan. By using the linear spline, we firstly estimates the time-varying proportion of cases who miss the nonpharmaceutical interventions (NPIs) among all reported cases. Assuming the reproduction numbers being 1.5, 2.0, 3.0, 4.0, 5.0 and 6.0, the respective probability of the end of the COVID-19 outbreak with time after the last reported case can be iteratively computed. Consequently, the varying reproduction numbers produce slightly different increasing patterns of NPI effectiveness, and the end-of-outbreak declarations with 95% confidence are projected consistently earlier than the day when the lockdown was actually lifted. The reason for the timing discrepancy is discussed as well.

While the vast majority of humans are able to entrain their circadian rhythm to the 24-h light-dark cycle, there are numerous individuals who are not able to do so due to disease or societal reasons. We use computational and mathematical methods to analyze a well-established model of human circadian rhythms to address cases where individuals do not entrain to the 24-h light-dark cycle, leading to misalignment of their circadian phase. For each case, we provide a mathematically justified strategy for how to minimize circadian misalignment. In the case of non-24-h sleep-wake disorder, we show why appropriately timed bright light therapy induces entrainment. With regard to shift work, we explain why reentrainment times following transitions between day and night shifts are asymmetric, and how higher light intensity enables unusually rapid reentrainment after certain transitions. Finally, with regard to teenagers who engage in compensatory catch-up sleep on weekends, we propose a rule of thumb for sleep and wake onset times that minimizes circadian misalignment due to this type of social jet lag. In all cases, the primary mathematical approach involves understanding the dynamics of entrainment maps that measure the phase of the entrained rhythm with respect to the daily onset of lights.

Soil fertility in mixed farming systems relies on the manure produced by livestock and its recycling in the entire system. In the particular case of crop-livestock system with grazing area, the proper functioning of the system also depends on the presence of nitrogen-fixing plants in the area where livestock grazes (the grazing land). In this paper, we study the impact of biological nitrogen fixation (BNF) and livestock management on the flux of manure exported outside the grazing land. We address this issue using a modeling approach. We consider a plant-soil model composed of a set of nonlinear ordinary differential equations that represents the grazing land. We assume that the manure produced by the grazing livestock can be partially exported as a fertilizer outside of this area. Through the mathematical analysis of the model, and analytical and numerical optimization, we then determine the optimal livestock management in terms of grazing rate and manure recycling percentage that lead to the maximal flux of exported manure. We focus more precisely on the role of nitrogen-fixing plants and their impact on the optimal livestock management. When grazing rate is high and the capacity of plants to fix nitrogen is important, we showed that it is necessary to recycle some of the manure produced by the livestock in the grazing land to maximize the flux of exported manure. On the contrary, if we can optimize both the grazing rate and the manure recycling percentage, then it is better to transfer all the produced manure and to adapt the grazing rate accordingly to minimize nitrogen losses from the soil. Finally, to maximize the flux of exported manure, it is also necessary to bring the system to a state in which the plants fix nitrogen. In this way, we can benefit from the nitrogen fixation which provides an additional input of nitrogen in the system.