Patterns arising from the reaction-diffusion epidemic model provide insightful aspects into the transmission of infectious diseases. For a classic SIR reaction-diffusion epidemic model, we review its Turing pattern formations with different transmission rates. A quantitative indicator, "normal serious prevalent area (NSPA)", is introduced to characterize the relationship between patterns and the extent of the epidemic. The extent of epidemic is positively correlated to NSPA. To effectively reduce NSPA of patterns under the large transmission rates, taken removed (recovery or isolation) rate as a control parameter, we consider the mathematical formulation and numerical solution of an optimal control problem for the SIR reaction-diffusion model. Numerical experiments demonstrate the effectiveness of our method in terms of control effect, control precision and control cost.

Public Goods Games (PGGs) are n-person games with dependence of individual fitness benefits on the collective investment by the players. We have studied a simple PGG scenario played out by cooperating (C) and defecting (D) agents, applying the highly nonlinear threshold benefit function in an individual-based lattice model. A semi-analytical approximation of the lattice model has been developed and shown to describe the dynamics fairly well in the vicinity of the steady state. Besides the expected outcomes (i.e., the negative effect on cooperator persistence of higher cooperation costs and/or more intensive mixing of the population) we have found a surprising, counter-intuitive effect of the strength of selection on the steady state of the model. The effect is different at low and high cooperation costs, and it shows up only in the lattice model, suggesting that stochastic effects and higher order spatial correlations due to the emergent spatial clustering of cooperators (not taken into account in the semi-analytical approximation) must be responsible for the unexpected results for which we propose an intuitive explanation, present a tentative demonstration, and shortly discuss their biological relevance.

Vaccination is effective in preventing human papillomavirus (HPV) infection. It still remains debatable whether males should be included in a vaccination program and unclear how to allocate the vaccine in genders to achieve the maximum benefits. In this paper, we use a two-sex model to assess HPV vaccination strategies and use the data from Guangxi Province in China as a case study. Both mathematical analysis and numerical simulations show that the basic reproduction number, an important indicator of the transmission potential of the infection, achieves its minimum when the priority of vaccination is given to the gender with a smaller recruit rate. Given a fixed amount of vaccine, splitting the vaccine evenly usually leads to a larger basic reproduction number and a higher prevalence of infection. Vaccination becomes less effective in reducing the infection once the vaccine amount exceeds the smaller recruit rate of the two genders. In the case study, we estimate the basic reproduction number is 1.0333 for HPV 16/18 in people aged 15-55. The minimal bivalent HPV vaccine needed for the disease prevalence to be below 0.05% is 24050 per year, which should be given to females. However, with this vaccination strategy it would require a very long time and a large amount of vaccine to achieve the goal. In contrast with allocating the same vaccine amount every year, we find that a variable vaccination strategy with more vaccine given in the beginning followed by less vaccine in later years can save time and total vaccine amount. The variable vaccination strategy illustrated in this study can help to better distribute the vaccine to reduce the HPV prevalence. Although this work is for HPV infection and the case study is for a province in China, the model, analysis and conclusions may be applicable to other sexually transmitted diseases in other regions or countries.

In this paper, we study the parkinson oscillation mechanism in a computational model by bifurcation analysis and numerical simulation. Oscillatory activities can be induced by abnormal coupling weights and delays. The bidirectional Hopf bifurcation phenomena are found in simulations, which can uniformly explain the oscillation mechanism in this model. The Hopf1 represents the transition between the low firing rate stable state (SS) and oscillation state (OS), the Hopf2 represents the transition between the high firing rate stable state (HSS) and the OS, the mechanisms of them are different. The Hopf1 and Hopf2 bifurcations both show that when the state transfers from the stable region to the oscillation region, oscillatory activities originate from the beta frequency band or the gamma frequency band. We find that the changing trends of the frequency (DF) and oscillation amplitude (OSAM) are contrary in many cases. The effect of the delay in inhibitory pathways is greater than that of in excitatory pathways, and appropriate delays improve the discharge activation level (DAL) of the system. In all, we infer that oscillations can be induced by the follow factors: 1. Improvement of the DAL of the globus pallidus externa (GPe); 2. Reduce the DAL of the GPe from the HSS or the discharge saturation state; 3. The GPe can also resonate with the subthalamic nucleus (STN).

Model-aided understanding of the mechanism of vegetation patterns and desertification is one of the burning issues in the management of sustainable ecosystems. A pioneering model of vegetation patterns was proposed by C. A. Klausmeier in 1999 (Klausmeier, 1999) that involves a downhill flow of water. In this paper, we study the diffusive Klausmeier model that can describe the flow of water in flat terrain incorporating a diffusive flow of water. It consists of a two-component reaction-diffusion system for water and plant biomass. The paper presents a numerical bifurcation analysis of stationary solutions of the diffusive Klausmeier model extensively. We numerically investigate the occurrence of diffusion-driven instability and how this depends on the parameters of the model. Finally, the model predicts some field observed vegetation patterns in a semiarid environment, e.g. spot, stripe (labyrinth), and gap patterns in the transitions from bare soil at low precipitation to homogeneous vegetation at high precipitation. Furthermore, we introduce a two-component reaction-diffusion model considering a bilinear interaction of plant and water instead of their cubic interaction. It is inspected that no diffusion-driven instability occurs as if vegetation patterns can be generated. This confirms that the diffusive Klausmeier model is the minimal reaction-diffusion model for the occurrence of vegetation patterns from the viewpoint of a two-component reaction-diffusion system.

Life is confronted with computation problems in a variety of domains including animal behavior, single-cell behavior, and embryonic development. Yet we currently do not know of a naturally existing biological system that is capable of universal computation, i.e., Turing-equivalent in scope. Generic finite-dimensional dynamical systems (which encompass most models of neural networks, intracellular signaling cascades, and gene regulatory networks) fall short of universal computation, but are assumed to be capable of explaining cognition and development. I present a class of models that bridge two concepts from distant fields: combinatory logic (or, equivalently, lambda calculus) and RNA molecular biology. A set of basic RNA editing rules can make it possible to compute any computable function with identical algorithmic complexity to that of Turing machines. The models do not assume extraordinarily complex molecular machinery or any processes that radically differ from what we already know to occur in cells. Distinct independent enzymes can mediate each of the rules and RNA molecules solve the problem of parenthesis matching through their secondary structure. In the most plausible of these models all of the editing rules can be implemented with merely cleavage and ligation operations at fixed positions relative to predefined motifs. This demonstrates that universal computation is well within the reach of molecular biology. It is therefore reasonable to assume that life has evolved - or possibly began with - a universal computer that yet remains to be discovered. The variety of seemingly unrelated computational problems across many scales can potentially be solved using the same RNA-based computation system. Experimental validation of this theory may immensely impact our understanding of memory, cognition, development, disease, evolution, and the early stages of life.

Fish live in water with a different osmotic pressure from that in the body. Their gills have chloride cells that transport ions to maintain an appropriate level of osmotic pressure in the body. The direction of ion transport is different between seawater and freshwater. There are two types of chloride cells that specialize in unidirectional transport and generalist cells that can switch their function quickly in response to environmental salinity. In species that experience salinity changes throughout life (euryhaline species), individuals may replace some chloride cells with cells of different types upon a sudden change in environmental salinity. In this paper, we develop a dynamic optimization model for the chloride cell composition of an individual living in an environment with randomly fluctuating salinity. The optimal solution is to minimize the sum of the workload of chloride cells in coping with the difference in osmotic pressure, the maintenance cost, and the temporal cost due to environmental change. The optimal fraction of generalist chloride cells increases with the frequency of salinity changes and the time needed for new cells to be fully functional but decreases with excess maintenance cost.

Autoimmune myocarditis is a rare, but frequently fatal, side effect of immune checkpoint inhibitors (ICIs), a class of cancer therapies. Despite extensive experimental work on the causes, development and progression of this disease, much still remains unknown about the importance of the different immunological pathways involved. We present a mathematical model of autoimmune myocarditis and the effects of ICIs on its development and progression to either resolution or chronic inflammation. From this, we gain a better understanding of the role of immune cells, cytokines and other components of the immune system in driving the cardiotoxicity of ICIs. We parameterise the model using existing data from the literature, and show that qualitative model behaviour is consistent with disease characteristics seen in patients in an ICI-free context. The bifurcation structures of the model show how the presence of ICIs increases the risk of developing autoimmune myocarditis. This predictive modelling approach is a first step towards determining treatment regimens that balance the benefits of treating cancer with the risk of developing autoimmune myocarditis.

Bone is a hard-soft biomaterial built through a self-assembly process under genetic regulatory network (GRN) monitoring. This paper aims to capture the behavior of the bone GRN part that controls mineralization by using a mathematical model. Here, we provide an advanced review of empirical evidence about interactions between gene coding (i) transcription factors and (ii) bone proteins. These interactions are modeled with nonlinear differential equations using Michaelis-Menten and Hill functions. Compared to empirical evidence - coming from osteoblasts culture -, the two best systems (among 126=2,985,984 possibilities) use factors of inhibition from the start of the activation of each gene. It reveals negative indirect interactions coming from either negative feedback loops or the recently depicted micro-RNAs. The difference between the two systems also lies in the BSP equation and two ways for activating and reducing its production. Thus, it highlights the critical role of BSP in the bone GRN that acts on bone mineralization. Our study provides the first theoretical evidence of osteoblast self-inhibition after activation of the genetic regulatory network controlling mineralization with this work.

Stem cell therapy is a promising treatment for the regeneration of myocardial tissue injured by an ischemic event. Mathematical modeling of myocardial regeneration via stem cell therapy is a challenging task, since the mechanisms underlying the processes involved in the treatment are not yet fully understood. Many aspects must be accounted for, such as the spread of stem cells and nutrients, chemoattraction, cell proliferation, stages of cell maturation, differentiation, angiogenesis, stochastic effects, just to name a few. In this paper we propose a 3D mathematical model with a free boundary that aims to provide a qualitative description of some main aspects of the stem cell regenerative therapy in a simplified scenario. The paper mainly focuses on the description of the shrinking of the necrotic core during treatment. The stem cell and nutrients dynamics are described through coupled reaction-diffusion problems. Proliferation, chemoattraction, tissue regeneration and nutrient consumption are included in the model.

Adequate cerebral blood flow has long been recognized as essential for the maintenance of the neuronal function while interruption of cerebral blood flow for durations as short as minutes can result in permanent brain damage. A primary goal of this work is to determine how a neuron's ability to respond to synaptic input depends on parameters that control cerebral blood flow. A complex mathematical model is constructed that integrates detailed biophysical models of neuronal action potentials, mitochondrial ATP production and cerebral capillary blood flow. The model also provides insights of the role of astrocytes in maintaining neuronal responses, as well as the impact of elevated cytosolic calcium, due to increased synaptic activity, on mitochondrial ATP production. Both dynamical systems analysis and numerical simulations are used to determine how the maximum frequency at which the neurons can respond to synaptic input depends on capillary blow flow, as well as the ability of astrocytes to buffer extracellular potassium and cytosolic calcium handling. Results are presented for both the cases of homogenous and heterogeneous capillary networks. These results demonstrate, through this interconnected model, that heterogeneity of the capillary flow results in a decrease in the ability of neurons to respond to synaptic stimulation and that intact glial function provides a further protective role for the neurons.

Malaria is a mosquito-borne disease with a devastating global impact. Plasmodium vivax is a major cause of human malaria beyond sub-Saharan Africa. Relapsing infections, driven by a reservoir of liver-stage parasites known as hypnozoites, present unique challenges for the control of P. vivax malaria. Following indeterminate dormancy periods, hypnozoites may activate to trigger relapses. Clearance of the hypnozoite reservoir through drug treatment (radical cure) has been proposed as a potential tool for the elimination of P. vivax malaria. Here, we introduce a stochastic, within-host model to jointly characterise hypnozoite and infection dynamics for an individual in a general transmission setting, allowing for radical cure. We begin by extending an existing activation-clearance model for a single hypnozoite, adapted to both short- and long-latency strains, to include drug treatment. We then embed this activation-clearance model in an epidemiological framework accounting for repeated mosquito inoculation and the administration of radical cure. By constructing an open network of infinite server queues, we derive analytic expressions for several quantities of epidemiological significance, including the size of the hypnozoite reservoir; the relapse rate; the relative contribution of relapses to the infection burden; the distribution of multiple infections; the cumulative number of recurrences over time, and the time to first recurrence following drug treatment. We derive from first principles the functional dependence between within-host and transmission parameters and patterns of blood- and liver-stage infection, whilst allowing for treatment under a mass drug administration regime. To yield population-level insights, our analytic within-host distributions can be embedded in multiscale models. Our work thus contributes to the epidemiological understanding of the effects of radical cure on P. vivax malaria.

Different species of scavengers may compete for the same food in an ecosystem. This case study considers the competition between jackals and vultures in Etosha National Park in Namibia. While jackals are facultative scavengers, able to hunt for food if necessary, vultures are obligate scavengers wholly dependent on carcasses of animals like zebras for persistence. This competition may be further affected by outbreaks of infections such as anthrax, which temporarily increase the number of carcasses but lower the zebra population, acting in some ways as a third competitor. We use a dynamical system to model the interplay between competition dynamics and infection dynamics, and how it is affected by the nature of the competition: indirect (exploitative) or direct (interference). A bifurcation analysis using reproduction numbers shows how vultures' survival may depend on their direct competitive edge in reaching carcasses faster than jackals, and how the infection and the scavengers complicate each other's persistence. Vultures' interference causes a backward bifurcation which enables them to persist. One possible outcome is a "strange bedfellows" bistability in which anthrax and vultures persist only together, not apart, despite being competitors.

Individual specialization and generalization refer to the breadth of prey types consumed by predators among all available prey. The ecological factors mechanistically determining individual differences and the coexistence of foraging strategies remain to be clarified. Formal quantitative models can elucidate the complex nonlinear mechanisms underlying predator-prey interactions. In this study, we built a dynamical model with multiple prey, with different nutritional values and reproductive rates, which are consumed by specialist and generalist predators. We then analyzed the viability of individual foraging strategies in all possible scenarios. Relative prey fertility and relative efficiency of predation, rather than prey nutritional value, determined the success of specialists and generalists. Less reproducing prey and the specialists relying on them face the highest danger of extinction, while generalists cannot thrive where specialists are sufficiently efficient in relation to the number of available prey. Our study provides new perspectives for empirical studies on individual specialization.

Many marine invertebrates have a benthic adult life with planktonic long feeding larval stages (planktotrophy). In other species, planktonic larvae do not eat, and after a rather short period, they settle and initiate their benthic stages (lecithotrophy). Still other species skip planktonic larval stages altogether, and adults produce benthic offspring (direct development). In this paper, we develop an evolutionary game among different life-cycle types and examine the conditions for each life-cycle type to win in a seasonal environment. The growth rate and mortality of benthic individuals are the same among all three life-cycle types, the local habitat (patches) for benthic individuals have a finite longevity, and adults may engage in a limited dispersal just before breeding. Planktotrophy evolves if the planktonic stages are more efficient in terms of biomass gain than benthic life. Otherwise, lecithotrophy or direct development should evolve. Among them, direct development is more advantageous than lecithotrophy if the cost of having planktonic larvae is large, the habitat for benthic individuals is stable, and adults engage in some dispersal.

After infecting a host, a viral strain may increase rapidly within the body and produce mutants with a faster proliferation rate than the virus itself. However, most of the mutants become extinct because of the stochasticity caused by the small number of infected cells. In addition, the mean growth rate of a mutant strain decreases with time because the number of susceptible target cells is reduced by the original strain. In this study, we calculated the fraction of mutants that can escape stochastic extinction, based on a continuous-time branching process with a time-dependent growth rate. We analyzed two cases differing in the mode of viral transmission: (1) an infected cell transmits the virus through cell-to-cell contact with a susceptible target cell; (2) an infected cell releases numerous free viral particles that subsequently infect susceptible target cells. The chance for a mutant strain to be established decreases with time after infection of the original type, and it may oscillate before convergence at the stationary value. We then calculated the probability of escaping stochastic extinction for a drug-resistant mutant when a patient received an antiviral drug that suppressed the original strain. Combining the rate of mutant production from the original strain and the chance of escaping stochastic extinction, the number of emerging drug-resistant mutations may have two peaks: one soon after the infection of the original type and the second at the start of antiviral drug administration.

Most models of selection incorporate some notion of environmental degradation where the majority of the population becomes less fit concerning a character resulting in pressure to adapt. Such models have been variously associated with an adaptation cost, the substitution load. Conversely, adaptative mutations that represent an improvement in fitness in the absence of environmental change have generally been assumed to be associated with negligible cost. However, such adaptations could represent a competitive advantage that diminishes resource availability for others and so induces a cost. This type of adaptation in the form of seedling competition has been suggested as a mechanism for increases in seed sizes during domestication, a trait associated with the standard stabilizing selection model. We present a novel cost framework for competitive selection that demonstrates significant differences in behaviour to environmental-based selection in intensity, intensity over time and directly contrasts with the expectations of the standard model. Grain metrics of nine archaeological crops fit a mixed model in which episodes of competitive selection often emerge from shifting optimum episodes of stabilizing selection, highlighting the potential prevalence of the mechanism outlined here and providing fundamental insight into the factors driving domestication.