Search

In the ecosystem, species need time to transform resources into energy for growth. In addition, the degradation period after species' mortality will lead to the reuse of resources. The two phenomena above contribute to the delay effects during the species' evolution. We here develop a turbidostat model incorporating delay effects to investigate the impact of resource consumption and reusing period on population evolution. We first analyze the existence and the stability of the positive equilibrium. Our results reveal the perturbation effect of delay parameters on its dynamics. When the time lag periods cross the critical values, the positive equilibrium becomes unstable, and periodic solutions are produced. The populations of the species will oscillate along with the resource consumption and recycling period. In addition, the multiple delay effect will decrease the negative effect of delay phenomenon on positive solutions. By controlling the delay period of decomposition, we can moderate the oscillations caused by the delay effect in resource consumption. To further understand the dynamics of periodic solutions, the direction of the Hopf bifurcation and the periodic solutions' stability are also discussed here. Several numerical examples are tested to validate the theoretical results in this work. [ABSTRACT FROM AUTHOR]

Competing populations within an ecosystem often release chemicals during the interactions and diffusion processes. These chemicals can have diverse effects on competitors, ranging from inhibition to stimulation of species' growth. This work constructs a competition model that incorporates stimulatory substances, spatial effects, and multiple time lags to investigate the combined impact of these phenomena on competitors' growth. When the stimulation rate from the produced chemicals falls within a suitable threshold interval, all species within the system can coexist. Under the species' coexistence, their diffusive phenomenon leads to a spatially heterogeneous distribution, resulting in patchy structures (Turing patterns) within their habitat. As the parameter values exceed their thresholds, species begin to exhibit spatially periodic oscillations (spatial Hopf bifurcation). The presence of multiple delays and competitors' diffusion contributes to spatially complex and heterogeneous behaviors (Turing–Hopf bifurcation). The results help us understand the underlying mechanisms behind these heterogeneous behaviors and enable us to mitigate their negative impact on species' growth and harvest. Numerical simulations are used to measure the dynamics of competitors under different parameter conditions. [ABSTRACT FROM AUTHOR]

Defective interfering particles (DIPs) are virus-like particles that occur naturally during virus infections. These particles are defective, lacking essential genetic materials for replication, but they can interact with the wild-type virus and potentially be used as therapeutic agents. However, the effect of DIPs on infection spread is still unclear due to complicated stochastic effects and nonlinear spatial dynamics. In this work, we develop a model with a new hybrid method to study the spatial-temporal dynamics of viruses and DIPs co-infections within hosts. We present two different scenarios of virus production and compare the results from deterministic and stochastic models to demonstrate how the stochastic effect is involved in the spatial dynamics of virus transmission. We compare the spread features of the virus in simulations and experiments, including the formation and the speed of virus spread and the emergence of stochastic patchy patterns of virus distribution. Our simulations simultaneously capture observed spatial spread features in the experimental data, including the spread rate of the virus and its patchiness. The results demonstrate that DIPs can slow down the growth of virus particles and make the spread of the virus more patchy. Author summary: Defective interfering particles (DIPs) are viral mutants in which a crucial part of the particle's genome has been lost. DIPs are not infectious but can still co-infect cells with natural viruses. Such mutations are not uncommon. In fact, it has been found in most classes of viruses, including SARS coronavirus and influenza virus. It gives DIPs a promising future as a medium for disease treatment. However, the mechanism by which DIPs affect virus transmission remains unclear. In this paper, we develop a model to study the interaction between viruses and DIPs within host cells and the role stochastic effects play in virus transmission. Our simulations can capture patchy patterns and other spatial spread features observed in experiments and demonstrate that DIPs can slow down the growth of virus particles and make the spread of viruses more patchy. [ABSTRACT FROM AUTHOR]

Demographic structure and latent phenomenon are two essential factors determining the rate of tuberculosis transmission. However, only a few mathematical models considered age structure coupling with disease stages of infectious individuals. This paper develops a system of delay partial differential equations to model tuberculosis transmission in a heterogeneous population. The system considers demographic structure coupling with the continuous development of disease stage, which is crucial for studying how aging affects tuberculosis dynamics and disease progression. Here, we determine the basic reproduction number, and several numerical simulations are used to investigate the influence of various progression rates on tuberculosis dynamics. Our results support that the aging effect on the disease progression rate contributes to tuberculosis permanence. [ABSTRACT FROM AUTHOR]

The transmission of production-limiting disease in farm, such as Neosporosis and Johne's disease, has brought a huge loss worldwide due to reproductive failure. This paper aims to provide a modeling framework for controlling the disease and investigating the spread dynamics of Neospora caninum -infected dairy as a case study. In particular, a dynamic model for production-limiting disease transmission in the farm is proposed. It incorporates the vertical and horizontal transmission routes and two vaccines. The threshold parameter, basic reproduction number $ \mathcal{R}_0 $, is derived and qualitatively used to explore the stability of the equilibria. Global stability of the disease-free and endemic equilibria is investigated using the comparison theorem or geometric approach. On the case study of Neospora caninum -infected dairy in Switzerland, sensitivity analysis of all involved parameters with respect to the basic reproduction number $ \mathcal{R}_0 $ has been performed. Through Pontryagin's maximum principle, the optimal control problem is discussed to determine the optimal vaccination coverage rate while minimizing the number of infected individuals and control cost at the same time. Moreover, numerical simulations are performed to support the analytical findings. The present study provides useful information on the understanding of production-limiting disease prevention on a farm. [ABSTRACT FROM AUTHOR]

Some industrial behaviors, such as wasting outputs and inadequately treated and stored hazardous materials, may pollute our environment, so some populations in the polluted habitats are at the edge of extinction. In this work, we develop a mathematical model that validates the dynamics of the food-chain population in a polluted environment with impulsive toxicant input. Based on the model, we obtain a sufficient condition for the extinction of populations. When the concentration of toxicants surpasses the threshold, it will contribute to the extinction of populations in the related environment. Also, sufficient conditions for the permanence of populations are obtained in our analysis. Several numerical simulations validate the theoretical conclusions and further reflect the influence of toxicants. [ABSTRACT FROM AUTHOR]

Neospora caninum (N. caninum) infection, one of the major causes of abortions in dairy cattle, has brought a huge loss to farmers worldwide. In this study, we develop a six-compartment susceptible-infected model of N. caninum transmission which is later reduced to a two-equation system. Potential controls including medication, test-and-cull, and vaccination are proposed and analyzed, and the corresponding reproduction numbers are derived. The conditions for the global stabilities of disease-free and endemic equilibria are investigated with analytical solutions and geometric approach. Furthermore, uncertainty and sensitivity analysis shows that three control strategies are effective towards the varied environment, whereas the effectiveness of each measure highly depends on parameters related to control actions. Dynamics of reproduction numbers illustrate that disease elimination can be achieved by three types of controls: (1) adopting medication with medicine efficacy higher than 0.4 to prevent vertical transmission, (2) implementing test-and-cull with culling coverage larger than 0.3, and (3) taking vaccine with coverage larger than 0.1. Numerical results suggest that preventive measures should at least include the prevention of access of other hosts, such as dogs, to cattle; otherwise, these control measures will lose effectiveness. Our presented study provides guidance for decision-making on N. caninum infected farm management. [ABSTRACT FROM AUTHOR]

In the microorganism cultivation process, delay and stochastic perturbations are inevitably accompanied, which results in complicated dynamical behaviors for microorganisms. In this paper, a mathematical model with discrete delay and random perturbation is constructed to understand how the dynamics of microorganisms in the turbidostat can be characterized. The existence, uniqueness and boundedness of the positive solution are first determined for the mathematical model. Furthermore, sufficient conditions for microorganism extinction and permanence in the turbidostat are obtained with the theory of stochastic differential equations. The system has the stationary distribution under a low-level intensity of stochastic perturbation from the environment; that is, microorganism in the turbidostat is persistent fluctuating around a positive value. On the contrary, microorganisms will be extinct with a strong enough intensity of noise. Several numerical simulations are applied to validate the theoretical results for the dynamics of the system. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) is a leading cause of death from infectious disease. TB is caused mainly by a bacterium called Mycobacterium tuberculosis which often initiates in the respiratory tract. The interaction of macrophages and T cells plays an important role in the immune response during TB infection. Recent experimental results support that active TB infection may be induced by the dysfunction of Treg cell regulation that provides a balance between anti-TB T cell responses and pathology. To better understand the dynamics of TB infection and Treg cell regulation, we build a mathematical model using a system of differential equations that qualitatively and quantitatively characterizes the dynamics of macrophages, Th1 and Treg cells during TB infection. For sufficiently analyzing the interaction between immune response and bacterial infection, we separate our model into several simple subsystems for further steady state and stability studies. Using this system, we explore the conditions of parameters for three situations, recovery, latent disease and active disease, during TB infection. Our numerical simulations support that Th1 cells and Treg cells play critical roles in TB infection: Th1 cells inhibit the number of infected macrophages to reduce the chance of active disease; Treg cell regulation reduces the immune response to stabilize the dynamics of the system. [ABSTRACT FROM AUTHOR]

Budding yeast, which undergoes polarized growth during budding and mating, has been a useful model system to study cell polarization. Bud sites are selected differently in haploid and diploid yeast cells: haploid cells bud in an axial manner, while diploid cells bud in a bipolar manner. While previous studies have been focused on the molecular details of the bud site selection and polarity establishment, not much is known about how different budding patterns give rise to different functions at the population level. In this paper, we develop a two-dimensional agent-based model to study budding yeast colonies with cell-type specific biological processes, such as budding, mating, mating type switch, consumption of nutrients, and cell death. The model demonstrates that the axial budding pattern enhances mating probability at an early stage and the bipolar budding pattern improves colony development under nutrient limitation. Our results suggest that the frequency of mating type switch might control the trade-off between diploidization and inbreeding. The effect of cellular aging is also studied through our model. Based on the simulations, colonies initiated by an aged haploid cell show declined mating probability at an early stage and recover as the rejuvenated offsprings become the majority. Colonies initiated with aged diploid cells do not show disadvantage in colony expansion possibly due to the fact that young cells contribute the most to colony expansion. [ABSTRACT FROM AUTHOR]

Crohn’s Disease (CD) results from inappropriate response toward commensal flora. Earlier studies described CD as a Th1 mediated disease. Current models view both phenotypes as a continuum of various permutations between Th1, Th2 and Th17 pathways compounded by a range of Treg disfunctions. In the present paper, we develop a mathematical model, by a system of differential equations, which describe the dynamic relations among these T cells and their cytokines. The model identities four groups of CD patients according to up/down regulation of Th1 and Th2. The model simulations show that immunosuppression by TNF-α blockage benefits the group with Th1High/Th2Low while, by contrast, the group with Th1Low/Th2High will benefit from immune activation. [ABSTRACT FROM AUTHOR]

Cdc42 plays a central role in establishing polarity in yeast and animals, yet how polarization of Cdc42 is achieved in response to spatial cues is poorly understood. Using live-cell imaging, we found distinct dynamics of Cdc42 polarization in haploid budding yeast in correlation with two temporal steps of the G1 phase. The position at which the Cdc42-GTP cluster develops changes rapidly around the division site during the first step but becomes stabilized in the second step, suggesting that an axis of polarized growth is determined in mid G1. Cdc42 polarization in the first step and its proper positioning depend on Rsr1 and its GTPase-activating protein (GAP) Bud2. Interestingly, Rga1, a Cdc42 GAP, exhibits transient localization to a site near the bud neck and to the division site during cytokinesis and G1, and this temporal change of Rga1 distribution is necessary for determination of a proper growth site. Mathematical modeling suggests that a proper axis of Cdc42 polarization in haploid cells might be established through a biphasic mechanism involving sequential positive feedback and transient negative feedback. [ABSTRACT FROM AUTHOR]

Cell polarization, in which intracellular substances are asymmetrically distributed, enables cells to carry out specialized functions. While cell polarity is often induced by intracellular or extracellular spatial cues, spontaneous polarization (the so-called symmetry breaking) may also occur in the absence of spatial cues. Many computational models have been used to investigate the mechanisms of symmetry breaking, and it was proved that spontaneous polarization occurs when the lateral diffusion of inactive signaling molecules is much faster than that of active signaling molecules. This conclusion leaves an important question of how, as observed in many biological systems, cell polarity emerges when active and inactive membrane-bound molecules diffuse at similar rates while cycling between cytoplasm and membrane takes place. The recent studies of Rätz and Röger showed that, when the cytosolic and membrane diffusion are very different, spontaneous polarization is possible even if the membrane-bound species diffuse at the same rate. In this paper, we formulate a two-equation non-local reaction-diffusion model with general forms of positive feedback. We apply Turing stability analysis to identify parameter conditions for achieving cell polarization. Our results show that spontaneous polarization can be achieved within some parameter ranges even when active and inactive signaling molecules diffuse at similar rates. In addition, different forms of positive feedback are explored to show that a non-local molecule-mediated feedback is important for sharping the localization as well as giving rise to fast dynamics to achieve robust polarization. [ABSTRACT FROM AUTHOR]

Gut mucosal homeostasis depends on complex interactions among the microbiota, the intestinal epithelium, and the gut associated immune system. A breakdown in some of these interactions may precipitate inflammation. Inflammatory bowel diseases, Crohn’s disease, and ulcerative colitis are chronic inflammatory disorders of the gastrointestinal tract. The initial stages of disease are marked by an abnormally high level of pro-inflammatory helper T cells, Th1. In later stages, Th2 helper cells may dominate while the Th1 response may dampen. The interaction among the T cells includes the regulatory T cells (Treg). The present paper develops a mathematical model by a system of differential equations with terms nonlocal in the space spanned by the concentrations of cytokines that represents the interaction among T cells through a cytokine signaling network. The model demonstrates how the abnormal levels of T cells observed in inflammatory bowel diseases can arise from abnormal regulation of Th1 and Th2 cells by Treg cells. [ABSTRACT FROM AUTHOR]

Cell polarization occurs along a single axis that is generally determined by a spatial cue. Cells of the budding yeast exhibit a characteristic pattern of budding, which depends on cell-type-specific cortical markers, reflecting a genetic programming for the site of cell polarization. The Cdc42 GTPase plays a key role in cell polarization in various cell types. Although previous studies in budding yeast suggested positive feedback loops whereby Cdc42 becomes polarized, these mechanisms do not include spatial cues, neglecting the normal patterns of budding. Here we combine live-cell imaging and mathematical modeling to understand how diploid daughter cells establish polarity preferentially at the pole distal to the previous division site. Live-cell imaging shows that daughter cells of diploids exhibit dynamic polarization of Cdc42-GTP, which localizes to the bud tip until the M phase, to the division site at cytokinesis, and then to the distal pole in the next G1 phase. The strong bias toward distal budding of daughter cells requires the distal-pole tag Bud8 and Rga1, a GTPase activating protein for Cdc42, which inhibits budding at the cytokinesis site. Unexpectedly, we also find that over 50% of daughter cells lacking Rga1 exhibit persistent Cdc42-GTP polarization at the bud tip and the distal pole, revealing an additional role of Rga1 in spatiotemporal regulation of Cdc42 and thus in the pattern of polarized growth. Mathematical modeling indeed reveals robust Cdc42-GTP clustering at the distal pole in diploid daughter cells despite random perturbation of the landmark cues. Moreover, modeling predicts different dynamics of Cdc42-GTP polarization when the landmark level and the initial level of Cdc42-GTP at the division site are perturbed by noise added in the model. [ABSTRACT FROM AUTHOR]