Journal of Mathematical Biology最新文献

Circadian clocks form a fundamental mechanism that promotes the correct behavior of many cellular and molecular processes by synchronizing them on a 24 h period. However, the circadian cycles remain difficult to describe mathematically. To overcome this problem, we first propose a segmentation of the circadian cycle into eight stages based on the levels of expression of the core clock components CLOCK:BMAL1, REV-ERB and PER:CRY. This cycle segmentation is next characterized through a piecewise affine model, whose analytical study allows us to propose an Algorithm to generate biologically-consistent circadian oscillators. Our study provides a characterization of the cycle dynamics in terms of four fundamental threshold parameters and one scaling parameter, shows robustness of the circadian system and its period, and identifies critical points for correct cycle progression.

Huanglongbing (HLB) is a bacterial disease that affects citrus trees worldwide. We present an innovative approach for identifying optimal control and risk measures for HLB in citrus orchards. Our method is based on a mathematical model that incorporates the number of roguing trees and a logistic growth model for the dynamic of the Asian Citrus Psyllid (ACP), the primary vector for HLB transmission. We derive an expression for: (1) the basic reproduction number $R_0$ ; (2) the final size for the number of roguing trees; and (3) the transmission risk. The above let us propose a difference map equation that assesses this final size with a low computational cost. We use this difference map in an evolutionary algorithm to identify the most effective combination of control parameter values for reducing HLB transmission, including the timing and frequency of roguing and the use of insecticides. In this sense, we propose two control strategies, which we called tree-centered and vector-centered.

Ben-Ari and Schinazi (J Stat Phys 162:415-425, 2016) introduced a stochastic model to study 'virus-like evolving population with high mutation rate'. This model is a birth and death model with an individual at birth being either a mutant with a random fitness parameter in [0, 1] or having one of the existing fitness parameters with uniform probability; whereas a death event removes the entire population of the least fitness. We change this to incorporate the notion of 'survival of the fittest', by requiring that a non-mutant individual, at birth, has a fitness according to a preferential attachment mechanism, i.e., it has a fitness f with a probability proportional to the size of the population of fitness f. Also death just removes one individual with the least fitness. This preferential attachment rule leads to a power law behaviour in the asymptotics, unlike the exponential behaviour obtained by Ben-Ari and Schinazi (J Stat Phys 162:415-425, 2016).

Models of ordinary differential equations are often used to describe the electrical, ionic and volumetric responses of cells to external stimuli. Although these cellular models are often solved numerically, rigorous evidence regarding their steady state solutions is scarce. In this work, we provide a formalism defining the conditions ensuring the existence and uniqueness of a steady-state solution in a large class of models including leak channels, a pump and cotransporters. Our work generalizes previous results and provides explicit conditions that a model must satisfy to guarantee the existence and uniqueness of a steady state.

We study a diffusive epidemic model and examine the spatial spreading dynamics of a multi-strain infectious disease. In particular, we address the questions of competitive-exclusion or coexistence of the disease's strains. Our results indicate that if one strain has its local reproduction function spatially homogeneous, which either strictly minimizes or maximizes the basic reproduction numbers, then the phenomenon of competitive-exclusion occurs. However, if all the local reproduction functions are spatially heterogeneous, several strains may coexist. In this case, we provide complete information on the large time behavior of classical solutions for the two-strain model when the diffusion rate is uniform within the population and the ratio of the local transmission rates is constant. Particularly, we prove the existence of two critical superimposed functions that serve as threshold values for the ratio of the transmission rates and that of the recovery rates. Furthermore, when the populations' diffusion rates are small, our result on the asymptotic profiles of coexistence endemic equilibria indicate a spatial segregation of infected populations.

Biological invasions significantly impact native ecosystems, altering ecological processes and community behaviors through predation and competition. The introduction of non-native species can lead to either coexistence or extinction within local habitats. Our research develops a lizard population model that integrates aspects of competition, intraguild predation, and the dispersal behavior of intraguild prey. We analyze the model to determine the existence and stability of various ecological equilibria, uncovering the potential for bistability under certain conditions. By employing the dispersal rate as a bifurcation parameter, we reveal complex bifurcation dynamics associated with the positive equilibrium. Additionally, we conduct a two-parameter bifurcation analysis to investigate the combined impact of dispersal and intraguild predation on ecological structures. Our findings indicate that intraguild predation not only influences the movement patterns of brown anoles but also plays a crucial role in sustaining the coexistence of different lizard species in diverse habitats.

Coupled Wright-Fisher diffusions have been recently introduced to model the temporal evolution of finitely-many allele frequencies at several loci. These are vectors of multidimensional diffusions whose dynamics are weakly coupled among loci through interaction coefficients, which make the reproductive rates for each allele depend on its frequencies at several loci. Here we consider the problem of filtering a coupled Wright-Fisher diffusion with parent-independent mutation, when this is seen as an unobserved signal in a hidden Markov model. We assume individuals are sampled multinomially at discrete times from the underlying population, whose type configuration at the loci is described by the diffusion states, and adapt recently introduced duality methods to derive the filtering and smoothing distributions. These respectively provide the conditional distribution of the diffusion states given past data, and that conditional on the entire dataset, and are key to be able to perform parameter inference on models of this type. We show that for this model these distributions are countable mixtures of tilted products of Dirichlet kernels, and describe their mixing weights and how these can be updated sequentially. The evaluation of the weights involves the transition probabilities of the dual process, which are not available in closed form. We lay out pseudo codes for the implementation of the algorithms, discuss how to handle the unavailable quantities, and briefly illustrate the procedure with synthetic data.

This paper is devoted to the study of optimal release strategies to control vector-borne diseases, such as dengue, Zika, chikungunya and malaria. Two techniques are considered: the sterile insect one (SIT), which consists in releasing sterilized males among wild vectors in order to perturb their reproduction, and the Wolbachia one (presently used mainly for mosquitoes), which consists in releasing vectors, that are infected with a bacterium limiting their vectorial capacity, in order to replace the wild population by one with reduced vectorial capacity. In each case, the time dynamics of the vector population is modeled by a system of ordinary differential equations in which the releases are represented by linear combinations of Dirac measures with positive coefficients determining their intensity. We introduce optimal control problems that we solve numerically using ad-hoc algorithms, based on writing first-order optimality conditions characterizing the best combination of Dirac measures. We then discuss the results obtained, focusing in particular on the complexity and efficiency of optimal controls and comparing the strategies obtained. Mathematical modeling can help testing a great number of scenarios that are potentially interesting in future interventions (even those that are orthogonal to the present strategies) but that would be hard, costly or even impossible to test in the field in present conditions.

A dynamical system obtains a wide variety of kinetic realizations, which is advantageous for the analysis of biochemical systems. A reaction network, derived from a dynamical system, may or may not possess some properties needed for a thorough analysis. We improve and extend the work of Johnston and Hong et al. on network translations to network transformations, where the network is modified while preserving the dynamical system. These transformations can shrink, extend, or retain the stoichiometric subspace. Here, we show that a positive dependent network can be translated to a weakly reversible network. Using the kinetic realizations of (1) calcium signaling in the olfactory system and (2) metabolic insulin signaling, we demonstrate the benefits of transformed systems with positive deficiency for analyzing biochemical systems. Furthermore, we present an algorithm for a network transformation of a weakly reversible non-complex factorizable kinetic (NFK) system to a weakly reversible complex factorizable kinetic (CFK) system, thereby enhancing the Subspace Coincidence Theorem for NFK systems of Nazareno et al. Finally, using the transformed kinetic realization of monolignol biosynthesis in Populus xylem, we study the structural and kinetic properties of transformed systems, including the invariance of concordance and variation of injectivity and mono-/multi-stationarity under network transformation.

Flow of cerebrospinal fluid through perivascular pathways in and around the brain may play a crucial role in brain metabolite clearance. While the driving forces of such flows remain enigmatic, experiments have shown that pulsatility is central. In this work, we present a novel network model for simulating pulsatile fluid flow in perivascular networks, taking the form of a system of Stokes-Brinkman equations posed over a perivascular graph. We apply this model to study physiological questions concerning the mechanisms governing perivascular fluid flow in branching vascular networks. Notably, our findings reveal that even long wavelength arterial pulsations can induce directional flow in asymmetric, branching perivascular networks. In addition, we establish fundamental mathematical and numerical properties of these Stokes-Brinkman network models, with particular attention to increasing graph order and complexity. By introducing weighted norms, we show the well-posedness and stability of primal and dual variational formulations of these equations, and that of mixed finite element discretizations.