The coronavirus disease (COVID-19) has infected more than 79 million individuals, with 1.7 million deaths worldwide. Several countries have implemented social distancing and testing policies with contact tracing as a measure to flatten the curve of the ongoing pandemic. Optimizing these control measures is urgent given the substantial societal and economic impacts associated with infection and interventions. To determine the optimal social distancing and testing strategies, we developed a mathematical model of COVID-19 transmission and applied optimal control theory, identifying the best approach to reduce the epidemiological burden of COVID-19 at a minimal cost. The results demonstrate that testing as a standalone optimal strategy does not have a significant effect on the final size of an epidemic, but it would delay the peak of the pandemic. If social distancing is the sole control strategy, it would be optimal to gradually increase the level of social distancing as the incidence curve of COVID-19 grows, and relax the measures after the curve has reached its peak. Compared with a single strategy, combined social distancing and testing strategies are demonstrated to be more efficient at reducing the disease burden, and they can delay the peak of the disease. To optimize these strategies, testing should be maintained at a maximum level in the early phases and after the peak of the epidemic, whereas social distancing should be intensified when the prevalence of the disease is greater than 15%. Accordingly, public health agencies should implement early testing and switch to social distancing when the incidence level begins to increase. After the peak of the pandemic, it would be optimal to gradually relax social distancing and switch back to testing.

We build a parsimonious Crump-Mode-Jagers continuous time branching process of COVID-19 propagation based on a negative binomial process subordinated by a gamma subordinator. By focusing on the stochastic nature of the process in small populations, our model provides decision making insight into mitigation strategies as an outbreak begins. Our model accommodates contact tracing and isolation, allowing for comparisons between different types of intervention. We emphasize a physical interpretation of the disease propagation throughout which affords analytical results for comparison to simulations. Our model provides a basis for decision makers to understand the likely trade-offs and consequences between alternative outbreak mitigation strategies particularly in office environments and confined work-spaces. Combining the asymptotic limit of our model with Bayesian hierarchical techniques, we provide US county level inferences for the reproduction number from cumulative case count data over July and August of this year.

Should theories of "higher-level" cognitive effects originate in "lower-level" molecular mechanisms? This paper supports reductionist explanations of sensory perception via molecular mechanisms in neurobiology. It shows that molecular and cellular mechanisms must constitute the material foundation to derive better theories and models for neuroscience. In support of "bottom-up theorizing", I explore the recent application of a new real-time molecular imaging technique (SCAPE microscopy) to mixture coding in olfaction. Seemingly emergent "higher-level" psychological effects in odor perception, irreducible to the physical stimulus, are linked back to underlying molecular mechanisms at the receptor level. The SCAPE study has notable theoretical impact. It provides a possible answer to the neurocomputational challenge in olfaction from combinatorial coding at the periphery: how does the brain discriminate different complex mixtures from widespread and overlapping receptor activation? The failure of previous reductionist structure-odor explanations is shown to reside in misconceptualizations of the critical causal elements involved. Causally fundamental features are not of parts independently of a mechanism. Components and their relevant features are units via their causal role within a mechanism. Here, new technologies allow revisiting our understanding of the ontology and levels of organization of a system.

In this work, we assess the impact of the phage-bacteria infection and optimal control on the indirectly transmitted cholera disease. The phage-bacteria interactions are described by predator-prey system using the Smith functional response, which takes into account the number of bacteria binding sites. The study is done in two steps, namely the model without control and the model with control. For the first scenario, we explicitly compute the basic reproduction number R0 which serves as stability threshold and bifurcation parameter. The proposed model exhibits a bi-stability phenomenon via the existence of backward bifurcation, which implies that the classical requirement of bringing the reproduction number under unity, while necessary, is no longer sufficient for cholera elimination from the population. We intuitively introduce a new threshold number N0 needed for the global stability of the disease free equilibrium point which is achieved when R0⩽1 and N0⩽1. It is further shown that the phage absorption is a possible cause of bi-stability, since in its absence, the condition R0⩽1 is sufficient for cholera to die out. The existence of endemic equilibrium points depends on the range of both R0 and N0. Regarding the model extended to an optimal control problem, which involves the use of virulent vibriophages to reduce or eliminate the bacteria population, we use optimal control theory techniques. We establish the conditions under which the spread of cholera can be stopped, and examine the impact of control measures on the transmission dynamic of cholera. The Pontryagin's maximum principle is used to characterize the optimal control. Numerical simulations suggest that, the release of lytic vibriophages can significantly reduce the spread of the disease. We discuss opportunities for phage therapy as treatment of some bacterial-borne diseases without side effects.

This work considers the propagation of a tumor from the stage of a small avascular sphere in a host tissue and the progressive onset of a tumor neovasculature stimulated by a pro-angiogenic factor secreted by hypoxic cells. The way new vessels are formed involves cell sprouting from pre-existing vessels and following a trail via a chemotactic mechanism (CM). Namely, it is first proposed a detailed general family of models of the CM, based on a statistical mechanics approach. The key hypothesis is that the CM is composed by two components: i) the well-known bias induced by the angiogenic factor gradient; ii) the presence of stochastic changes of the velocity direction, thus giving rise to a diffusive component. Then, some further assumptions and simplifications are applied in order to derive a specific model to be used in the simulations. The tumor progression is favored by its acidic aggression towards the healthy cells. The model includes the evolution of many biological and chemical species. Numerical simulations show the onset of a traveling wave eventually replacing the host tissue with a fully vascularized tumor. The results of simulations agree with experimental measures of the vasculature density in tumors, even in the case of particularly hypoxic tumors.

A honey bee can dip nectar of viscosity across two orders of magnitude, by viscous lapping technique using a segmental tongue covered with erectable hairs. The drinking technique suffers risks of leakage occurring between tongue hairs, and the amount of leakage is related to hair spacing as well as nectar viscosity. When lapping, tongue segments are elongated, which enlarges the hair spacing in longitudinal direction. Experimental observations show that the hair spacing of tongue increases with respect to sucrose solution concentration until it reaches the maximum extension when sucrose solution concentration is above 35%. Considering leakage occurring in the hairy tongue, we hypothesize that the dynamical extension of hair spacing may help honey bees minimize the effects of leakage to reach maximal nectar intake rate. A mathematical model is developed for determining the optimal hair spacing that can meet the demands of both augmenting the nectar intake rate and reducing the risk of leakage. Theoretical prediction and experimental measurements demonstrate honey bees are able to adjust the tongue to meet the optimal hair spacing when dipping nectar of concentration more dilute than 35% and maintain a maximum extension to improve the nectar intake rate when concentration is greater than 35%. We then give the prediction of concentration preferences of three bee species, and discuss effects of dipping frequency and gravity on the leakiness between tongue hairs. This work may not only gain insights into adaptive feeding strategy in insects, but inspire the design of adaptive microfluidic transport devices with dynamic brushy surfaces.

We developed a tumor control probability (TCP) model that incorporates variable time intervals between fractions and a kick-off time (Tk) for radiation-induced accelerated tumor proliferation. The resulting Lee-Rosen model, TCPLR, was used to compute TCPs for treatment courses with and without weekend treatment for tumors with different proliferation rates - slow (prostate), moderate (breast), and rapid (head and neck). TCPs were computed using ideal uniform dose distributions and actual patient plans. The doses for the uniform plans were the mean doses for the prostate and breast cases and the minimum tumor dose for the head and neck case. The TCPLR model predictions agreed with expectations that TCP increases with increasing Tk in all cases. For standard fractionation, as Tk increased from 0 to 4 weeks, TCP increased for the patient distributions by 74.7% for the head and neck cancer, by 6.2% for the breast cancer, and by 2.4% for the prostate cancers. For the uniform dose distributions, the increases were 79.2%, 5.7%, and 2.3%, respectively. TCP increased as the number of weekend breaks decreased. The effect of weekend breaks decreased as the tumor proliferation rate decreased. For the head and neck tumor, notable decreases in TCP of 6.0% (uniform dose distribution) and 6.8% (actual plan dose distribution) were observed with Friday starts compared to Monday starts for the standard 5 fx/wk schedule (Tk = 4 wk). The 7 fx/wk schedule produced increases in TCP of 17.0% and 20.5% for the uniform and patient dose distributions, respectively, compared to the standard schedule. For the breast cancer, starting the 5 fx/wk schedule on Friday decreased the TCP by 0.2% (Tk = 4 wk) compared to a Monday start. The 7 fx/wk schedule produced increases of 0.3% and 0.4% in TCP compared to the standard schedule for the uniform and patient dose distributions, respectively (Tk = 4 wk). For the prostate cancer, the change in TCP for 5 fx/wk schedules starting on different days was 0.1%. The 7 fx/wk schedule increased TCP by 0.8% compared to the standard schedule (Tk = 4 wk). TCP values for the uniform dose distributions for the standard schedule (Tk = 4 wk) agreed with the TCP values for the actual dose distributions within 4.5% for the head and neck tumor and within 0.2% for the breast and prostate tumors. This good agreement suggests that the doses chosen for the uniform dose distributions were good approximations to the clinical doses. The results for head and neck tumors support, in part, the current practice of hyperfractionated/accelerated radiotherapy. They also suggest that shortening the overall treatment time for conventional fractions by eliminating weekend breaks might be beneficial. The predicted effect on TCP of the various schedules studied was insignificant for prostate and breast tumors, suggesting that a weekend treatment might not be necessary for patients starting radiotherapy on a Friday. There is significant uncertainty in the values of the model parameters chosen for these calculations, and no consideration was given to the potential effects of these various schedules on normal tissues.

Maternal selection and overlapping generations can facilitate the stable coexistence of alleles under temporally fluctuating environment. Using mathematical models, we considered the complex effect of both factors on the maintenance of genetic polymorphism in cyclically changing environments. We concentrated on asymmetric cyclic selection, which allows describing fluctuations of environments by analogy of food resources cycles with rare peaks and prolonged decline of prey abundance. The complex effect of maternal selection and overlapping generations turned out to work as follows: although overlapping generations always tend to dilate the polymorphism region, odd and even external cycles produce different types of polymorphism regions. Maternal selection under external odd cycles extends the coexistence region comparing with classic selection. Even cycles produce a part of parameter region, where the picture changes radically, and classic selection becomes more effective in maintaining polymorphism. Our models have clear biological interpretation, because we tried to model a situation demonstrated by natural populations of arctic foxes. The litter size being a major life history trait is a sex-limited female trait. It is influenced by maternal selection with cyclical fluctuations because of oscillations in food abundance. Arctic fox is a long-lived species having an age structure. The obtained results showed that compared with the simple Mendelian inheritance in the classic model, this trait inheritance allows polymorphism to be maintained in a wider range of the parameter that characterizes the advantage of survival in a small litter. Besides, adding overlapping generations to the model further broadens the parameter space for the protected polymorphism. Thus, this study shows that maternal selection and overlapping generations increases the chances of maintaining polymorphism in populations of arctic foxes.

In China, foot-and-mouth disease (FMD) serotype O remains prevalent, and its main host is pigs. Infected but undiscovered pigs can carry foot-and-mouth disease virus (FMDV) for a longtime. And, the virus can spread among farms through pig trade. Although individual vaccination at least 2 times a year and monthly monitoring disease and culling all individual in same group for pigs are adopted vigorously in China, the epidemic remains prevalent. Therefore, in this paper, based on these propagation characteristics and control measures of the epidemic in China, we take the pig farms as research individuals, the trade among farms as transmission routes to establish a dynamic model with nonlinear incidence. In addition, we use this model to assess the impact of trade and transport of pigs among farms on the spread of foot-and-mouth disease virus (FMDV), and to assess the effect of the immunization, monitoring and culling adopted presently in China on the control of the epidemic. By the dynamical analysis of the model, it is found that there will appear backward branching under some conditions, which means that there are two spreading thresholds for the disease, and the disease development trend is also related to the current epidemic situation. Besides, we give the threshold conditions of key parameters to control the spread of FMD. By carrying out data fitting and parameter estimation, we confirm the model rationality, and give four evaluation indexes: the basic reproduction number R0 of FMD serotype O in China, the value of the infected farms at the equilibria, annual probability of a susceptible farm being infected and annual transmission intensity of an infected farm. By carrying out the sensitivity analysis of key parameters on four evaluation indexes, the effect of parameters on the spread of the disease can be intuitively observed. All these can provide a theoretical basis for understanding of the trading-based transmission mechanism, control and prevention of foot-and-mouth disease in pigs in China.

Motile cells depend on an intricate network of feedback loops that are essential in driving cell movement. Integrin-based focal adhesions (FAs) along with actin are the two key factors that mediate such motile behaviour. Together, they generate excitable dynamics that are essential for forming protrusions at the leading edge of the cell and, in certain cases, traveling waves along the membrane. A partial differential equation (PDE) model of a self-organizing lamellipodium in crawling keratocytes has been previously developed to understand how the three spatiotemporal patterns of activity observed in such cells, namely, stalling, waving and smooth motility, are produced. The model consisted of three key variables: the density of barbed actin filaments, newly formed FAs called nascent adhesions (NAs) and VASP, an anti-capping protein that gets sequestered by NAs during maturation. Using parameter sweeping techniques, the distinct regimes of behaviour associated with the three activity patterns were identified. In this study, we convert the PDE model into an ordinary differential equation (ODE) model to examine its excitability properties and determine all the patterns of activity exhibited by this system. Our results reveal that there are two additional regimes not previously identified, including bistability and oscillatory-like type IV excitability (generated by three steady states and their manifolds, rather than limit cycles). These regimes are also present in the PDE model. Applying slow-fast analysis on the ODE model shows that it exhibits a canard explosion through a folded-saddle and that rough motility seen in keratocytes is likely due to noise-dependent motility governed by dynamics near the interface of bistability and type IV excitability. The two parameter bifurcation suggests that the increase in the proportion of rough motion is due to a shift in activity towards the bistable and type IV excitable regimes induced by a decrease in NA maturation rate. Our results thus provide important insight into how microscopic mechanical effects are integrated to produce the observed modes of motility.

Update of ArXiv. 2020 Jul 15;:

Murray's law, which states that the cube of the radius of a parent vessel equals the sum of the cubes of the radii of the daughter vessels, was originally derived by minimizing the cost of operation of blood flow in a single cylindrical tube. An alternative widely cited derivation by Sherman is based upon the optimization problem of minimizing the total flow resistance subject to a material constraint, and that study claimed that "Conservation of the sum of the cubes of the radii is the condition for minimal resistance whether the parent vessel divides symmetrically or asymmetrically, and whether it divides into two, three, four, or, presumably, any number of daughter vessels." In this paper we show that Sherman's analysis is flawed, since with N daughter vessels there are 2N-N-1 sets of vessel radii which satisfy Murray's law but which do not yield minimal total flow resistance. Moreover, we show that when there are N daughter vessels, each with the same radius, the minimal total flow resistance is an increasing function of N for N⩾1. Since N=1 corresponds to the degenerate case of no branching at all, our result implies that bifurcation (N=2) achieves the minimal total flow resistance. Our analysis thus offers an explanation for the preponderance of bifurcations (as opposed to trifurcations or higher level branchings) in many biological systems.

Many herbaceous plants feature remarkably regular arrangements of lateral organs along the central axis. These phyllotactic patterns are generated by a constant divergence angle between successive buds (or whorls thereof) that first appears at the shoot apircal meristem and is maintained across later ontogentic stages when it can be observed at the macroscopic scale. Do the branches along a tree trunk exhibit similar patterns? Here we use branch skeleton data derived from terrestrial laser scans to empirically estimate the distributions of the divergence angles between successive branches along the trunks of mature European beech, Norway spruce, and Scots pine trees. We find that rather than clustering around a particular value, species-specific branch divergence angles feature statistical properties characteristic of a uniform distribution. We hypothesise this to be the result of the stochasticity in bud development and branch shedding, and provide a rigorous mathematical proof that even when the divergence angle between successive lateral buds is constant, the observed distribution of branch divergence angles will approximate a uniform distribution if bud mortality and branch shedding rates are high.

Multiple sclerosis is an autoimmune disease that affects white matter in the central nervous system. It is one of the primary causes of neurological disability among young people. Its characteristic pathological lesion is called a plaque, a zone of inflammatory activity and tissue destruction that expands radially outward by destroying the myelin and oligodendrocytes of white matter. The present paper develops a mathematical model of the multiple sclerosis plaques. Although these plaques do not provide reliable information of the clinical disability in MS, they are nevertheless useful as a primary outcome measure of Phase II trials. The model consists of a system of partial differential equations in a simplified geometry of the lesion, consisting of three domains: perivascular space, demyelinated plaque, and white matter. The model describes the activity of various pro- and anti-inflammatory cells and cytokines in the plaque, and quantifies their effect on plaque growth. We show that volume growth of plaques are in qualitative agreement with reported clinical studies of several currently used drugs. We then use the model to explore treatments with combinations of such drugs, and with experimental drugs. We finally consider the benefits of early vs. delayed treatment.

In this paper we develop an SEIR-type model of COVID-19, with account for two particular aspects: non-exponential distribution of incubation and recovery periods, as well as age structure of the population. For the mean-field model, which does not distinguish between different age groups, we demonstrate that including a more realistic Gamma distribution of incubation and recovery periods may not have an effect on the total number of deaths and the overall size of an epidemic, but it has a major effect in terms of increasing the peak numbers of infected and critical care cases, as well as on changing the timescales of an epidemic, both in terms of time to reach the peak, and the overall duration of an outbreak. In order to obtain more accurate estimates of disease progression and investigate different strategies for introducing and lifting the lockdown, we have also considered an age-structured version of the model, which has allowed us to include more accurate data on age-specific rates of hospitalisation and COVID-19 related mortality. Applying this model to three comparable neighbouring regions in the UK has delivered some fascinating insights regarding the effect of lockdown in regions with different population structure. We have discovered that for a fixed lockdown duration, the timing of its start is very important in the sense that the second epidemic wave after lifting the lockdown can be significantly smaller or larger depending on the specific population structure. Also, the later the fixed-duration lockdown is introduced, the smaller is the resulting final number of deaths at the end of the outbreak. When the lockdown is introduced simultaneously for all regions, increasing lockdown duration postpones and slightly reduces the epidemic peak, though without noticeable differences in peak magnitude between different lockdown durations.

Androdioecy, the coexistence of hermaphrodites and males, is very rare in vertebrates but occurs in mangrove killifish living in ephemeral or unstable habitats. Hermaphrodites reproduce both by outcrossing with males and by selfing. Outbreeding is advantageous because of inbreeding depression, but it requires encounters with males. The advantages of a propensity for outcrossing among hermaphrodites and the production of males affect each other very strongly. To study the evolutionary coupling of these two aspects, we here analyze a simple evolutionary game for a population composed of three phenotypes: outcrossing-oriented hermaphrodites, selfing-oriented hermaphrodites, and males. Outcrossing-oriented hermaphrodites first attempt to search for males and perform outcrossing if they encounter males. If they fail to encounter males, they reproduce via selfing. Selfing-oriented hermaphrodites simply reproduce by selfing. The replicator dynamics may show bistability, in which both the androdioecious population (with outcrossing-oriented hermaphrodites and males) and the pure hermaphroditic population are locally stable. The model shows the fraction of males is either zero or relatively high (more than 25%), which is not consistent with the observed low fraction of males (less than 5%). To explain this discrepancy, we studied several models including immigration and enforced copulation. We concluded that the observed pattern can be most likely explained by a population dominated by selfing-oriented hermaphrodites receiving immigration of males.

Classical studies in evolutionary game theory assume constant payoffs. Randomly fluctuating environments in real populations make this assumption idealistic. In this paper, we study randomized two-player linear games in a finite population in a succession of birth-death events according to a Moran process and in the presence of symmetric mutation. Introducing identity measures under neutrality that depend on the mutation rate and calculating these in the limit of a large population size by using the coalescent process, we study the first-order effect of the means, variances and covariances of the payoffs on average abundance in the stationary state under mutation and selection. This shows how the average abundance of a strategy is driven not only by its mean payoffs but also by the variances and covariances of its payoffs. In Prisoner's Dilemmas with additive cost and benefit for cooperation, where constant payoffs always favor the abundance of defection, stochastic fluctuations in the payoffs can change the strategy that is more abundant on average in the stationary state. The average abundance of cooperation is increased if the variance of any payoff to cooperation against cooperation or defection, or their covariance, is decreased, or if the variance of any payoff to defection against cooperation or defection, or their covariance, is increased. This is also the case for a Prisoner's Dilemma with independent payoffs that is repeated a random number of times. As for the mutation rate, it comes into play in the coefficients of the variances and covariances that determine average abundance. Increasing the mutation rate can enhance or lessen the condition for a strategy to be more abundant on average than another.

Oxygenic photoautotrophs are, paradoxically, subject to photoinhibition of their photosynthetic apparatus, in particular one of its major components, the Photosystem II (PSII). Photoinhibition is generalized across species, light conditions and habitats, imposing substantial metabolic costs that lower photosynthetic productivity and constrain the niches of photoautotrophy. As a process driven by light reaching PSII, light attenuation in optically thick samples influences both the actual extent, and the detection, of photoinhibition. Chlorophyll fluorescence is widely used to measure photoinhibition, but fluorescence-based parameters are affected by light attenuation of both downwelling incident radiation traversing the sample to reach PSII, and emitted fluorescence upwelling through the sample. We used modelling, experimental manipulation of within-sample light attenuation, and meta-analysis of published data, to show substantial, differential effects of light attenuation and depth-integration of emitted fluorescence upon measurements of photoinhibition. Numerical simulations and experimental manipulation of light attenuation indicated that PSII photoinactivation tracked using chlorophyll fluorescence can appear to be over three times lower than the inherent cellular susceptibility to photoinactivation, in optically-dense samples such as leaves or biofilms. The meta-analysis of published data showed that this general trend was unknowingly present in the literature, revealing an overall difference of more than five times between optically thick leaves and optically thin cell suspensions. Although fluorescence-based parameters may provide ecophysiologically relevant information for characterizing the sample as a whole, light attenuation and depth integration can vary between samples independently of their intrinsic physiology. They should be used with caution when aiming to quantify in absolute terms inherent photoinhibition-related parameters in optically thick samples.