In this paper, we study a model about non-toxic phytoplankton (NTP), toxin-producing phytoplankton (TPP), and zooplankton defined on a two-dimensional circular domain with predator-taxis and time-delay. The relationship between NTP, TPP and zooplankton is explored by combining selective grazing, cannibalism, Allee effect and additional food. For the proposed model, a rigorous proof of global solution existence with uniform boundedness is provided. By applying the Brouwer fixed-point theorem, we demonstrate the existence of a positive constant steady-state solution. Within the functional analytic framework, we establish conditions for both standard and equivariant Hopf bifurcations occurring in the neighborhood of the spatially homogeneous equilibrium. Next we obtain the existence condition and specific properties of periodic solutions by bifurcation theory and normal form method. Numerically, we select appropriate parameters with practical significance and validate analytical predictions via computational experiments. Specifically, we show different types of rotating waves and standing waves, which are the rather complex dynamic behaviors in the two-dimensional circular domain. And then we reveal the periodic phenomena of NTP, TPP and zooplankton, as well as biological phenomena caused by selective grazing, cannibalism, Allee effect and additional food, which provides valuable results for monitoring and controlling the distribution of plankton populations and protecting aquatic ecosystems.
We introduce a magnetic extension of the Hückel molecular orbital (HMO) method in which the effect of an external magnetic field is incorporated through the Peierls substitution. In this formulation, the π -electron Hamiltonian of a conjugated molecule becomes a complex-weighted hopping operator defined on the hydrogen-depleted molecular graph. Under the standard Hückel assumptions, this operator coincides with the Hermitian adjacency matrix of the graph, providing a physical realization of Hermitian adjacency operators within molecular electronic structure theory. The magnetic-HMO framework enables the calculation of flux-dependent electronic observables such as bond currents, ring currents, orbital magnetization, and orbital susceptibility directly from the spectrum of the magnetic adjacency matrix. Applications to polycyclic aromatic hydrocarbons show that the magnetic response of π -electron systems is strongly controlled by molecular topology. In particular, linearly fused systems exhibit regular flux-dependent oscillations in the orbital magnetization, whereas nonlinear and extended molecules display more complex spectral rearrangements associated with multiple conjugation pathways. MSC (2020): 05C50; 92E10; 81Q10; 05C90.
This work focuses on feedback control strategies for applying the sterile insect technique (SIT) to eliminate pest populations. The presentation is centered on the case of mosquito populations, but most of the results can be extended to other species by adapting the model and selecting appropriate parameter values to describe the reproduction and movement dynamics of the species under consideration. In our study, we address the spatial distribution of the population in a two dimensional bounded domain by extending the temporal SIT model analyzed in [2], thereby obtaining a reaction-diffusion SIT model. After the analysis of the existence and the uniqueness of the solution of this problem, we construct a feedback law that globally asymptotically stabilizes the extinction equilibrium thus yielding a robust strategy to keep the pest population at very low levels in the long term. p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Helvetica; color: #000000}
The nonlinear mechanisms underlying the emergence of plankton patchiness have attracted considerable attention in recent decades. In this research, a coupled reaction-diffusion model for phytoplankton-zooplankton interactions is developed by incorporating plankton migration across water layers. Conditions for pattern self-organization are derived through stability analysis, and robustness of multiscale pattern regimes is quantified through local and global sensitivity analyses. When the dispersion relation has multiple peaks, both pure Turing and Hopf-Turing instabilities can generate patterns with two or three coexisting patch sizes. Variance spectrum analysis on the multiscale patterns shows a power-law distribution of plankton variance across spatial scales. Using 1 km as a dividing scale, pure Turing instability mainly shapes smaller-scale patchiness, whereas Hopf-Turing instability has a stronger influence at larger scales. By introducing spatially heterogeneous carrying capacity, the self-organized patterns show variance spectra with slopes comparable to those reported in the literature. Additional tests with nutrient limitation and turbulence demonstrate that multiscale patchiness persists under more realistic forcing, and comparison with chlorophyll-a spectra from the Bohai and Yellow Seas supports the model ability to reproduce scaling behavior. These findings suggest that Turing instability and environmental heterogeneity can jointly provide a plausible mechanism for multiscale plankton patchiness observed in natural ecosystems.
Microbial decomposition of organic matter in soil is a fundamental process in the global carbon cycle, directly influencing soil health, fertility, and greenhouse gas emissions. This paper presents a dynamic analysis and numerical simulation of a reaction-diffusion model that describes microbial decomposition of organic matter within a three dimensional soil structure. We investigate the interactions between Microbial Biomass (MB) and organic substrates, as well as the diffusion of various compounds through the soil matrix, using nonlinear parabolic partial differential equations. Our study provides proofs for the existence and uniqueness of solutions, as well as an analysis of asymptotic behavior. Notably, our investigation reveals the presence of a global attractor, where any solution, regardless of initial conditions, tends to converge. To illustrate the practical implications of our findings, we have developed a numerical tool to simulate the long-term behavior of the system with reasonable computational expense. This tool provides a visual proof of the global attractor for a validated set of biological parameters in a real sandy loam soil sample captured using 3D tomography imagery.
This work focuses on modeling adhesive haptotaxis in cell migration. While cells typically move toward regions of high adhesiveness, experiments on lymphocytes at the Laboratory of Adhesion & Inflammation (LAI) in Marseille have revealed an opposite behavior known as reverse adhesive hap-totaxis. To investigate this phenomenon, we adapt a single-cell migration model originally proposed by Aronson and Ziebert [Soft Matter 10 (2014) 1365-1373, PLoS One 8 (2013) 1-14, J. Roy. Soc. Interface 9 (2012) 1084-1092], which accounts for the dynamics of adhesion site density. In our adaptation, we exclude contractility and rear adhesion—factors likely irrelevant for lymphocyte propulsion [Aoun et al., Biophys. J. 119 (2020) 1157-1177] - and explore the role of adhesion signaling in two key processes: (i) propulsion at the cell front, as previously proposed in Ziebert and Aranson [PLoS One 8 (2013) 1-14], and (ii) actin polymerization within the cell, a novel aspect of this study. By thoroughly analyzing the interplay between these mechanisms, we demonstrate that our model can capture both classical and reverse haptotaxis. Notably, reverse haptotaxis emerges in this context when propulsion is coupled with positive feedback signaling mechanism but also when actin polymerization is coupled with negative feedback mechanism, suggesting the need for future experimental efforts to identify the corresponding signaling cascade in lymphocytes.
This work investigates the long-term dynamics of a novel predator-prey system that explicitly accounts for age structure, Beddington-Deangelis functional response, constant-yield prey harvesting, and two distinct time delays. The first delay, tau 1 denotes the predator's maturation period; the second, tau 2 reflects the gestation delay between prey consumption and predator reproduction. Firstly, we recast the system into an abstract non-densely defined Cauchy problem. Then the existence of solutions and the uniqueness of positive equilibrium are discussed. By analyzing the distribution of the corresponding eigenvalues, the rigorous establishment of asymptotic stability for the boundary equilibria are achieved. We further present a detailed Hopf bifurcation analysis that simultaneously incorporates both time-delay parameters, employing stability-switching curves to clarify how varying delays reshape the system's dynamic behavior. Lastly, the practical implications of these theoretical findings are demonstrated through several numerical examples.
Malaria and typhoid fever are major infectious diseases that pose significant public health challenges in many parts of the world, particularly in sub-Saharan Africa. This study develops a mathematical model to investigate the dynamics of malaria-typhoid co-infection, incorporating both vector and non-vector malaria transmission routes and environmental transmission for typhoid. Model parameters were drawn from the literature, and simulations were conducted in MATLAB. The results show that vector-borne transmission accounts for over 80% of malaria infections, while typhoid transmission sustains a persistent infection level. Co-infected individuals constitute approximately 25-35% of the total infected population at peak conditions, underscoring the substantial burden of simultaneous infection. Sensitivity analysis identifies malaria and typhoid transmission rates as key drivers of co-infection prevalence. A backward bifurcation in the malaria subsystem indicates that malaria may persist even when its reproduction number is below one, thereby continually seeding co-infection and indirectly maintaining typhoid transmission through co-infected individuals. These findings highlight the need for integrated and sustained control strategies, including vector control, typhoid vaccination, and improved sanitation, to effectively reduce the dual disease burden. Overall, the model provides a useful analytical framework to support public health planning and evidence-based resource allocation in regions where both infections remain endemic.
We introduce a set of ordinary differential equations (ODE) that qualitatively reproduces delayed responses observed in immune checkpoint blockade therapy, such as anti-CTLA-4 Ipilimumab. Immune checkpoint inhibitors have revolutionised cancer treatment, offering durable responses in some patients, but their efficacy is often hindered by delayed anti-tumour immune responses. Our ODE system can be considered as two modular submodels: one focusing on dendritic cell (DC) dynamics within the tumour microenvironment and the other on T cell activation within lymph nodes. Together, these submodels provide a mechanistic framework to explore the interplay between immune activation and tumour-driven suppression. By calibrating key parameters, our models naturally reproduce clinically observed phenomena that range from no response to delayed anti-tumour activity. Simulations suggest that insufficient co-stimulatory signals by DCs may play a key role in delayed responses. Furthermore, we offer a framework on how individual immune profiles shape treatment outcomes in anti-CTLA-4 and anti-PD-1 combination therapies. Our model also suggests potential insights into long-term dynamics, including tumour dormancy, oscillatory behaviour and the conditions necessary for durable tumour eradication. We hope this exploratory study will inspire further research into the intricate and nuanced dynamics of tumour-immune interactions.
In this study, a plant-herbivore model with double time delays and double Allee effects was constructed, incorporating intraspecific competition among herbivores. Theoretical analyses established the existence conditions of the positive equilibrium point and the boundedness of solutions. The stability and Hopf bifurcation of equilibria in the non-delayed system were thoroughly investigated, and the existence of Hopf bifurcations and global stability under double delays were examined. Numerical simulations demonstrated that when delays exceed critical thresholds, Hopf bifurcations occur, leading to system instability. Double Allee effects were shown to exacerbate this process, with increasing Allee intensity reducing plant population density.
This paper proposes a new method for solving a class of high-dimensional partially linear varying coefficient model. Firstly, an adaptive elastic net regularization term is added to the partially linear varying coefficient model to obtain a new model. This model improves the accuracy of the model by adjusting the parameter weights. Then, the ADMM method is used to solve the model parameters, and the convergence of the algorithm is analyzed. Subsequently, numerical simulations are conducted on high-dimensional datasets to demonstrate the effectiveness of the proposed method. Finally, the proposed method is applied to practical cases for testing and analysis, further verifying its effectiveness and application value.
This paper investigates the effect of stochastic perturbations on the deterministic UEV framework, which characterizes the problem of unemployment in poor countries. It examines how the system behaves and stays stable under random fluctuations. We study the existence and uniqueness of the non-negative solution. Furthermore, we examine the asymptotic behavior of this solution by analyzing the stability of the system at equilibrium points under some conditions. Finally, some numerical simulations are performed to verify the theoretical analysis using Matlab.
Several major epidemic events over the past two decades have highlighted the importance of developing and studying non-Markovian compartmental models. [T. Sellke, J. Appl. Probab. 20 (1983) 390-394] introduced an ingenious construction for the SIR epidemic process to study the final size of epidemics. In this paper, we extend this construction to the SEI1I2RS model. This model is chosen for its compactness, while including parallel infectious stages (I1 and I2) and cycles (aka loops) due to reinfection. Our methodology easily generalizes to a general class of stochastic compartmental models in closed populations, including SIR-like models (a series of compartments in one row), SEIAR-like models (parallel compartments), but also models with cycles. Our construction inherits from Sellke construction its ability to handle both Markovian and non-Markovian frameworks. Also, it naturally leads to a representation of the epidemic process under the form of a deterministic function of uncertain parameters (such as epidemic parameters) and variables modeling internal noise. Based on this representation, we propose a global sensitivity analysis of the SEI1I2RS model. With our methodology we are able to quantify epistemic uncertainty due to the lack of knowledge on epidemic parameters and statistical uncertainty induced by stochasticity of the model. Finally we provide numerical experiments in both Markovian and non-Markovian frameworks.
Many viral capsids are varieties of icosahedral-like polyhedra. The production of many mature viral capsids involves folding an RNA-tethered set of a string of identical proteinaceous cap-someres. The initial configuration of such tethered collections can be represented as DUrer nets which are planar graphs of cuts of polyhedra. While there are only 2 D & uuml;rer nets of a tetrahedron and 11 D & uuml;rer nets each of a cube and an octahedron, there are 43 380 Durer nets each of a dodecahedron and an icosahedron. If various Durer nets are three dimensionally printed in two layers in plastic sheets with magnets on each edge and then are placed in warm water, some configurations self-fold into completed polyhedra. Unfortunately, while some configurations self-fold easily to completion in a short interval, others self-intersect and are unable to close into a complete polyhedron. These four- dimensional printing experiments have previously only allowed us to explore a few configurations. Here we report on using an origami simulator where we could investigate the folding of numerous Du & uuml;rer nets. We found that two topological invariants: the diameter of spanning trees and number of vertex connections of a Durer net, had a significant impact on the time of folding to completion. Also, more symmetrical Durer nets fold faster and to completion than more irregular configurations. This research has relevance to biomimetic design particularly to employing nanocapsules made of viral capsids ("virosomes") as carriers of drugs in medical applications.
The synthetic indolinone derivative MAZ-51 is a selective inhibitor of vascular endothelial growth factor receptor 3 (VEGFR-3), a tyrosine kinase receptor essential for lymphangiogenesis and tumor progression. By competing with adenosine triphosphate (ATP) for VEGFR-3 binding, MAZ-51 blocks VEGF-C activity, thereby suppressing melanoma cell proliferation and promoting apoptosis. In this study, we employ mathematical modelling to quantify the inhibitory effects of MAZ-51 on the growth of B16-F10 melanoma cells. Cell viability is modeled as a function of both treatment duration and inhibitor concentration, providing a dynamic framework for assessing therapeutic efficacy. Our approach addresses a central challenge in mathematical biology: developing models that remain interpretable and predictive despite limited and variable data. By integrating biological insight with experimental data, we derive a parsimonious model that avoids overparameterization and yields biologically meaningful parameters. The model allows straightforward computation of pharmacological measures such as the half-maximal inhibitory concentration (IC50) and provides deeper insight into the growth rate reduction of melanoma cells under VEGFR-3 inhibition. This work highlights the utility of mathematical modelling in elucidating drug action mechanisms and in quantitatively evaluating targeted cancer therapies.
This paper is motivated by the need to model the dynamics of liquid–vapor flows involving phase transitions in heat exchangers. In the low Mach number asymptotic limit, we derive a system of 1D conservation laws with heat transfers causing phase change, with a degenerate and nonlinear thermal diffusion coefficient. This degeneracy induces discontinuities on the solution, both on the enthalpy and the velocity. We provide explicit steady and travelling wave solutions, and derive suitable numerical schemes able to capture the moving discontinuities.
Stent implantation is a standard treatment for iliac vein compression syndrome (IVCS), but the stented vein remains vulnerable to persistent lesions, which can result in adverse outcomes. These complications are often linked to complex vascular abnormalities apart from the stent segment, influenced by lower limb movements and physical stimuli. This study aims to investigate the hemodynamic consequences of persistent lesions and the effects of various therapeutic strategies after post-stenting. A patient-specific model was developed to simulate flattened lesions, narrow lesions, and tissue adhesions (TA), enabling an analysis of hemodynamic parameters such as Wall Shear Stress (WSS), Oscillatory Shear Index (OSI), Relative Residence Time (RRT), and Flow Resistance (RF) in the post-intervention environment. The results reveal that contralateral venous lesions, including flattened lesions, narrow lesions, and tissue adhesions, significantly worsen the hemodynamic conditions in the iliac vein after stenting. Furthermore, the study demonstrates that both active ankle exercises (AAE) and intermittent pneumatic compression (IPC) therapies can improve the hemodynamic environment in the stented vein. However, these therapies may also inadvertently exacerbate blood flow disturbances at the contralateral lesion site. These findings emphasize the need for tailored therapeutic strategies that account for residual lesions to optimize clinical outcomes post-stenting.
We provided in this work a theoretical framework to study and to simulate the population dynamics of Busseola fusca (B. fusca): maize pest. The aim is to simulate and predict the presence levels of Busseola fusca under the influence of temperature variations and control actions. Based on the life cycle of B. fusca), we first propose a mathematical model to study the population dynamics of this maize pest. Some parameters are taken to be temperature-dependent. This led to a system of non-autonomous differential equations. Also, the classical control strategies are incorporated in the model. We present the theoretical analysis of the model. For the model with constant parameters, we compute the basic offspring number N-0 that determines the evolution of the population of this insect and establish that the trivial equilibrium is globally asymptotically stable whenever N-0 < 1, while if N-0 > 1, the non trivial equilibrium is globally asymptotically stable. For the model with temperature variations, we find two explicit thresholds parameters N-max and N-min that bound the basic offspring number N-0 (such that N-max <= N-0 <= N-min), and use them to prove the extinction and the persistence of the pest within a maize field. We prove analytically and by numerical simulations that B. fusca) persists uniformly within a maize field when N-min > 1 and tends to disappears within a maize field when N-max < 1. The theoretical results are illustrated by numerical simulations. They suggest further that spraying insecticides to kill larvae and destroying residues after harvest significantly reduce the population Busseola fusca more than other control actions.
Adaptive therapy improves cancer treatment by controlling the competition between sensitive and resistant cells through treatment holidays. This study highlights the role of treatment-holidays and the treatment-restarting thresholds in adaptive therapy for tumours composed of drug-sensitive and resistant cells. Using a Lotka-Volterra model, adaptive therapy outcomes are compared with maximum tolerated dose therapy and intermittent therapy outcomes, showing that adaptive therapy success depends critically on the thresholds for pausing and resuming treatment and on competitive interactions between cell populations. Three comparison scenarios between adaptive therapy and other therapies emerge, including uniform-decline where adaptive therapy underperforms regardless of threshold, conditional-improve where efficacy requires threshold optimisation, and uniform-improve where adaptive therapy consistently outperforms alternatives. Tumour initial conditions such as initial burden and initial resistant cell proportion influence outcomes. Threshold adjustments enable adaptive therapy to suppress resistant subclones while preserving sensitive cells, extending progression-free survival. Crucially, this work establishes an optimal control problem for time-to-progression and mathematically proves that under biological constraints like neutral competition or low initial burden, the theoretically optimal strategy is unrealisable as it requires infinitely many treatment holidays, rendering it clinically impractical. These findings emphasize personalised treatment strategies for enhancing long-term therapeutic outcomes.
