Journal of Biological Dynamics最新文献

This study examines competition models based on the Lotka-Volterra form that incorporate starvation-driven diffusions (SDD). Such dispersal assumes that species disperse in response to resource abundance or scarcity in a heterogeneous habitat. The primary objective of this study is to examine how SDD, in combination with diverse interspecific interactions, affects species' fitness and coexistence states. To this end, the study introduces a refined classification for competing interactions based on a novel metric that quantifies the variability of resource heterogeneity across the environment. This approach contrasts with traditional models that assume uniform diffusion within homogeneous environments. This study investigates the local stability of two semitrivial steady states and establishes the existence and uniqueness of positive steady states by eigenvalue analysis and monotone dynamical systems theory. Through this analytical exploration, the study reveals that the interplay between species' dispersal strategies and the varying intensities of interspecific competition significantly impacts ecological outcomes.

This work examines the dynamics of a discrete-time plankton interaction model, in which phytoplankton generate toxins and are vulnerable to external contamination. The model includes a Holling Type-II predation response and uses a piecewise constant argument approach to break it up into smaller pieces. This keeps the ecological realism of the continuous system while making it possible to study complex discrete-time behaviors. Our focus is on the formation of Neimark-Sacker bifurcation, a phenomena associated with the initiation of quasi-periodic oscillations in population densities. We show how toxin buildup and outside contamination can make plankton populations unstable, which could cause blooms to happen in an irregular way, using stability analysis and numerical simulations. The results show how useful discrete-time models are for capturing rapid changes in ecosystems, such damaging algal blooms. They also give ideas for managing ecosystems and reducing blooms.

To study the macroscopic dynamics of susceptible host cells, infected host cells, free virus particles and antibodies after viral infection within-host, this study develops a novel dynamic model that integrates three key mechanisms: a general incidence function capturing the complexity of antibody production, the inhibitory effect of antibodies on viral infectivity and the cytokine-mediated self-cure of infected cells. The basic reproduction numbers for both the virus and immune response are derived, along with sufficient conditions for the stability of equilibria. Bifurcation analysis revealed that a Hopf bifurcation may occur when the basic reproduction number of the immune response exceeds one. Numerical simulations highlight the critical role of saturation effects in viral replication and the immune response for infection control. Antibody immunity, once depleted, may not be replenished and neglecting saturation effects could overestimate both the oscillatory parameter range and the severity of infection.

COVID-19 infection exhibits significant age-related differences. In this paper, we consider an infectious disease model with age-structure in susceptibility and evolutionary game and analyze the impact of mandatory and voluntary vaccination strategies on disease progression. We derive the conditions for the existence of equilibria and confirm that the basic reproduction number $R_0$ serves as a threshold parameter that fully determines the dynamical properties of the model. Theoretical analyses indicate that the persistence of COVID-19 is contingent upon the value of the basic reproduction number. By conducting numerical simulations, we investigate the impacts of various factors, including relative vaccine cost and vaccine effectiveness, on disease dynamics under a voluntary vaccination policy. Our analysis reveals that enhancing vaccine effectiveness does not reduce disease transmission when vaccination rates are extremely low. Under voluntary vaccination policies, it is crucial to keep relative vaccine costs below a certain threshold to promote higher vaccination uptake.

Based on the considerations of round-trip in the treatment process, this paper presents a mathematical model aimed at studying the dynamic behaviour and epidemiological trends of HIV/AIDS. We first calculate the basic reproduction number ${\bar{R}}_0$ and discuss the stability of equilibrium points and the existence of forward bifurcations, validating the theoretical results through numerical simulations. Subsequently, using cumulative HIV/AIDS case data reported in China, we estimate model parameters using the least squares method, achieving a good fit. Furthermore, sensitivity analyses were performed on the model parameters to explain the dependence of the parameters on the infection variables. Finally, the model is applied to evaluate the control effects of treatment coverage at different stages of infection. The results suggest that reducing HIV/AIDS exposure, improving HIV/AIDS screening, promoting infectious disease treatment and increasing disease prevention awareness are the most effective measures to prevent HIV/AIDS infection.

Determining optimal antibiotic dosing strategies is complex. Clinically, some antibiotics work best in continuous low doses, while others require high repeated pulses. However, a rational understanding of the best approach depending on the specific pairing of antibiotics and bacterial species remains unclear. Using mathematical models, we analyze bacterial populations under two strategies-constant concentration and repeated dosing-with fixed pharmacodynamic and pharmacokinetic properties. Our results reveal that the shape of the dose‒response curve, which measures the bacterial net growth rate against the antibiotic concentration, is crucial. Specifically, its concavity determines the best strategy. In cases where the curve exhibits multiple concavities, additional factors, such as the tolerable dosing range, influence the regimen. These findings challenge the universal application of 'hit hard and hit early', as some recommended schedules include lower, constant doses. This work contributes to the literature on rational antibiotic prescription, aiming to minimize antibiotic use and combat antimicrobial resistance.

We study periodic dynamics and error-threshold behavior in a delayed quasispecies model consisting of a master sequence $\left(x_0\right)$ and two mutant populations $(x_1,x_2)$. The system, formulated as delay differential equations with time-periodic replication rates, yields new conditions for the existence and absence of $T$-periodic solutions. Using topological degree arguments, we show that when mutation probabilities $\left(Q_{\mathrm{ji}}\right)$ lie strictly between 0 and 1 and at least one fitness function $\left(f_j\right)$ is periodic, the system supports nontrivial positive periodic orbits, with or without backward mutations. This shows that fluctuating environments, such as circadian or treatment-induced cycles, can sustain oscillatory genotype distributions. Conversely, if mutations are strictly unidirectional and the master sequence is consistently dominated in fitness, no positive $T$-periodic orbit arises. In this regime, the master sequence decays monotonically to extinction without time delays, while time delays induce non-monotonic decay, recovering the classical error-threshold phenomenon and linking it to cancer-related quasispecies dynamics.

We extend the predator-prey model developed by Ackleh et al. [Persistence and stability analysis of discrete-time predator-prey models: A study of population and evolutionary dynamics. J. Differ. Equ. Appl. 2019;25:1568-1603] to incorporate the evolution of a predator's resistance to toxicant effects. We consider three cases: (1) lethal effects, where the toxicant directly influences the predator's survival; (2) sublethal effects, where the toxicant impacts the predator's fecundity, and (3) mixed effects, where the toxicant impacts both vital rates. For the first two cases, we derive conditions for existence and stability of model equilibria and for system persistence. These cases are also analyzed numerically to further understand the system dynamics. Overall, we find that evolution of a predator to resist a toxicant may allow for predator survival when otherwise it would have faced extinction. However, evolution in response to lethal effects can generate multiple boundary equilibria, leading to alternative stable states. When this occurs, evolution in response to a toxicant may result in the extinction of the predator while, without evolution, the predator survives.

Hepatitis B transmission is influenced by environmental variability, immune response and vaccination, making its spread inherently stochastic, while the integration of stochastic modeling with machine learning is particularly important for representing disease uncertainty in varied surroundings. We present a hybrid innovative framework that combines a stochastic epidemiological model with a feed-forward neural network to study hepatitis B virus (HBV) dynamics. We show the well-posedness by establishing the existence of solutions with uniqueness, and analyze extinction and persistence of the disease. In addition, a supervised approach of feed-forward neural network (FFNN) having two hidden layers, each consist of 20 neurons will be used to effectively approximate the dynamics of the model. To evaluate robustness of the network while handling the stochastic model, we evaluate the performance by regression and mean squared error (MSE), and to show a strong alliance among the stochastic trajectories and predicted simulations obtained by the neural network.

In this paper, we introduce a mathematical simulation that captures the dynamics of lumpy skin disease (LSD) by considering three key transmission paths: vector-borne, direct cattle-to-cattle contact and environmental contamination. Additionally, this model incorporates three control measures, including vector control, environmental management and isolation/treatment of infected cattle. We perform a comprehensive mathematical analysis to demonstrate the model well-posedness, like proving the existence, uniqueness, positivity and boundedness of the solution. The basic reproduction number ($R_0$) is calculated. The local and global stability analysis is presented for the disease-free and endemic equilibrium points. Sensitivity analysis for the model parameters is shown, which reveals that isolation and treatment control measures are the most effective in eliminating disease transmission. We construct an objective function to formulate an optimal control problem (OCP) and derive the optimality necessary conditions. Numerical simulations confirm the theoretical findings, demonstrating that strategic implementation of combined control measures can efficiently suppress LSD.