Mathematical Biosciences最新文献

Understanding the consequences on population dynamics of the variability in dispersal over a fragmented habitat remains a major focus of ecological and environmental inquiry. Dispersal is often asymmetric: wind, marine currents, rivers, or human activities produce a preferential direction of dispersal between connected patches. Here, we study how this asymmetry affects population dynamics by considering a discrete-time two-patch model with asymmetric dispersal. We conduct a rigorous analysis of the model and describe all the possible response scenarios of the total realized asymptotic population abundance to a change in the dispersal rate for a fixed symmetry level. In addition, we discuss which of these scenarios can be achieved just by restricting mobility in one specific direction. Moreover, we also report that changing the order of events does not alter the population dynamics in our model, contrary to other situations discussed in the literature.

We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA into protein. The processes in sub-cellular compartments are described by an arbitrary number of processing stages, thus accounting for a significantly finer molecular description of gene expression than conventional models such as the telegraph, two-stage and three-stage models of gene expression. We use two distinct tools, queueing theory and model reduction using the slow-scale linear-noise approximation, to derive exact or approximate analytic expressions for the moments or distributions of nuclear mRNA, cytoplasmic mRNA and protein fluctuations, as well as lower bounds for their Fano factors in steady-state conditions. We use these to study the phase diagram of the stochastic model; in particular we derive parametric conditions determining three types of transitions in the properties of mRNA fluctuations: from sub-Poissonian to super-Poissonian noise, from high noise in the nucleus to high noise in the cytoplasm, and from a monotonic increase to a monotonic decrease of the Fano factor with the number of processing stages. In contrast, protein fluctuations are always super-Poissonian and show weak dependence on the number of mRNA processing stages. Our results delineate the region of parameter space where conventional models give qualitatively incorrect results and provide insight into how the number of processing stages, e.g. the number of rate-limiting steps in initiation, splicing and mRNA degradation, shape stochastic gene expression by modulation of molecular memory.

We classify connected 2-node excitatory–inhibitory networks under various conditions. We assume that, as well as for connections, there are two distinct node-types, excitatory and inhibitory. In our classification we consider four different types of excitatory–inhibitory networks: restricted, partially restricted, unrestricted and completely unrestricted. For each type we give two different classifications. Using results on ODE-equivalence and minimality, we classify the ODE-classes and present a minimal representative for each ODE-class. We also classify all the networks with valence $\le 2$. These classifications are up to renumbering of nodes and the interchange of ‘excitatory’ and ‘inhibitory’ on nodes and arrows. These classifications constitute a first step towards analysing dynamics and bifurcations of excitatory–inhibitory networks. The results have potential applications to biological network models, especially neuronal networks, gene regulatory networks, and synthetic gene networks.

Phytoplankton bloom received considerable attention for many decades. Different approaches have been used to explain the bloom phenomena. In this paper, we study a Nutrient–Phytoplankton–Zooplankton (NPZ) model consisting of a periodic driving force in the growth rate of phytoplankton due to solar radiation and analyse the dynamics of the corresponding autonomous and non-autonomous systems in different parametric regions. Then we introduce a novel aspect to extend the model by incorporating another periodic driving force into the growth term of the phytoplankton due to sea surface temperature (SST), a key point of innovation. Temperature dependency of the maximum growth rate (${\mu }_{max}$) of the phytoplankton is modelled by the well-known $Q_{10}$ formulation: ${\mu }_{max}={\mu }_0\ast {\left(Q_{10}\right)}^{T/10}$, where ${\mu }_0$ is maximum growth at $0^o$C. Stability conditions for all three equilibrium points are expressed in terms of the new parameter ${\rho }_2$, which appears due to the incorporation of periodic driving forces. System dynamics is explored through a detailed bifurcation analysis, both mathematically and numerically, with respect to the light and temperature dependent phytoplankton growth response. Bloom phenomenon is explained by the saddle point bloom mechanism even when the co-existing equilibrium point does not exist for some values of ${\rho }_2$. Solar radiation and SST are modelled using sinusoidal functions constructed from satellite data. Our results of the proposed model describe the initiation of the phytoplankton bloom better than an existing model for the region 25–35° W, 40–45° N of the North Atlantic Ocean. An improvement of 14 days (approximately) is observed in the bloom initiation time. The rate of change method (ROC) is applied to predict the bloom initiation.

Physicians prescribe empiric antibiotic treatment when definitive knowledge of the pathogen causing an infection is lacking. The options of empiric treatment can be largely divided into broad- and narrow-spectrum antibiotics. Prescribing a broad-spectrum antibiotic increases the chances of covering the causative pathogen, and hence benefits the current patient’s recovery. However, prescription of broad-spectrum antibiotics also accelerates the expansion of antibiotic resistance, potentially harming future patients. We analyse the social dilemma using game theory. In our game model, physicians choose between prescribing broad and narrow-spectrum antibiotics to their patients. Their decisions rely on the probability of an infection by a resistant pathogen before definitive laboratory results are available. We prove that whenever the equilibrium strategies differ from the socially optimal policy, the deviation is always towards a more excessive use of the broad-spectrum antibiotic. We further show that if prescribing broad-spectrum antibiotics only to patients with a high probability of resistant infection is the socially optimal policy, then decentralization of the decision making may make this policy individually irrational, and thus sabotage its implementation. We discuss the importance of improving the probabilistic information available to the physician and promoting centralized decision making.

This paper deals with a diffusive population-toxicant model in polluted aquatic environments, with a toxicant-taxis term describing a toxicant-induced behavior change, that is, the population tends to move away from locations with high-level toxicants. The global existence of solutions is established by the techniques of the semigroup estimation and Moser iteration. Based on a detailed study on the properties of the principal eigenvalue for non-self-adjoint eigenvalue problems, we investigated the local and global stability of the toxin-only steady-state solution and the existence of positive steady state, which yields sufficient conditions that lead to population persistence or extinction. Finally, by numerical simulations, we studied the effects of some key parameters, such as toxicant-taxis coefficient, advection rate, and effect coefficient of the toxicant on population growth, on population persistence. Both numerical and analytical results show that a weak chemotaxis effect, a small advection rate of the population, and a weak effect of the toxicant on population growth are favorable for population persistence.

Computational models of brain regions are crucial for understanding neuronal network dynamics and the emergence of cognitive functions. However, current supercomputing limitations hinder the implementation of large networks with millions of morphological and biophysical accurate neurons. Consequently, research has focused on simplified spiking neuron models, ranging from the computationally fast Leaky Integrate and Fire (LIF) linear models to more sophisticated non-linear implementations like Adaptive Exponential (AdEX) and Izhikevic models, through Generalized Leaky Integrate and Fire (GLIF) approaches. However, in almost all cases, these models are tuned (and can be validated) only under constant current injections and they may not, in general, also reproduce experimental findings under variable currents. This study introduces an Adaptive GLIF (A-GLIF) approach that addresses this limitation by incorporating a new set of update rules. The extended A-GLIF model successfully reproduces both constant and variable current inputs, and it was validated against the results obtained using a biophysical accurate model neuron. This enhancement provides researchers with a tool to optimize spiking neuron models using classic experimental traces under constant current injections, reliably predicting responses to synaptic inputs, which can be confidently used for large-scale network implementations.

We investigated a system of ordinary differential equations that describes the dynamics of prey and predator populations, taking into account the Allee effect affecting the reproduction of the predator population, and mutual interference amongst predators, which is modeled with the Bazykin–Crowley–Martin (BCM) trophic function. Bifurcation analysis revealed a rich spectrum of bifurcations occurring in the system. In particular, analytical conditions for the saddle–node, Hopf, cusp, and Bogdanov–Takens bifurcations were derived for the model parameters, quantifying the strength of the predator interference, the Allee effect, and the predation efficiency. Numerical simulations verify and illustrate the analytical findings. The main purpose of the study was to test whether the mutual interference in the model with BCM trophic function provides a stabilizing or destabilizing effect on the system dynamics. The obtained results suggest that the model demonstrates qualitatively the same pattern concerning varying the interference strength as other predator-dependent models: both low and very high interference levels increase the risk of predator extinction, while moderate interference has a favorable effect on the stability and resilience of the prey–predator system.

This paper proposes a bidimensional modeling framework for Wolbachia invasion, assuming imperfect maternal transmission, incomplete cytoplasmic incompatibility, and direct infection loss due to thermal stress. Our model adapts to various Wolbachia strains and retains all properties of higher-dimensional models. The conditions for the durable coexistence of Wolbachia-carrying and wild mosquitoes are expressed using the model’s parameters in a compact closed form. When the Wolbachia bacterium is locally established, the size of the remanent wild population can be assessed by a direct formula derived from the model. The model was tested for four Wolbachia strains undergoing laboratory and field trials to control mosquito-borne diseases: wMel, wMelPop, wAlbB, and wAu. As all these bacterial strains affect the individual fitness of mosquito hosts differently and exhibit different levels of resistance to temperature variations, the model helped to conclude that: (1) the wMel strain spreads faster in wild mosquito populations; (2) the wMelPop exhibits lower resilience but also guarantees the smallest size of the remanent wild population; (3) the wAlbB strain performs better at higher ambient temperatures than others; (4) the wAu strain is not sustainable and cannot persist in the wild mosquito population despite its resistance to high temperatures.

Antibiotics Time Machine is an important problem to understand antibiotic resistance and how it can be reversed. Mathematically, it can be modeled as follows: Consider a set of genotypes, each of which contain a set of mutated and unmutated genes. Suppose that a set of growth rate measurements of each genotype under a set of antibiotics is given. The transition probabilities of a ‘realization’ of a Markov chain associated with each arc under each antibiotic are computable via a predefined function given the growth rate realizations. The aim is to maximize the expected probability of reaching to the genotype with all unmutated genes given the initial genotype in a predetermined number of transitions, considering the following two sources of uncertainties: (i) the randomness in growth rates, (ii) the randomness in transition probabilities, which are functions of growth rates. We develop stochastic mixed-integer linear programming and dynamic programming approaches to solve static and dynamic versions of the Antibiotics Time Machine Problem under the aforementioned uncertainties. We adapt a Sample Average Approximation approach that exploits the special structure of the problem and provide accurate solutions that perform very well in an out-of-sample analysis.