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.

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.

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.

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.

Human T-lymphotropic virus (HTLV) and human immunodeficiency virus (HIV) are two retroviruses that pose a certain threat to human psychology and physiology. In this paper, we propose a diffusive HTLV and HIV coinfection model with macrophages, two delays, cell-to-cell transmission and three latently infected cells in which latent HIV infected CD4${}^{+}$T cells, latent HIV infected macrophages, and latent HTLV infected CD4${}^{+}$T cells are considered. Four reproduction number and four equilibria, namely, infection-free equilibrium, HIV infection equilibrium, HTLV infection equilibrium and HTLV and HIV coinfection equilibrium, are calculated and proved the global asymptotic stability of the coinfection model. Numerical simulations are executed to showcase the corresponding theoretical outcomes and uncover how macrophages and latently infected cells influence the dynamics of HTLV and HIV coinfection.

In this paper, we analyze a deterministic model of malaria and Corona Virus Disease 2019 co-infection within a homogeneous population. We first studied the single infection model of each disease and then the co-infection dynamics. We calculate the basic reproduction number of each model and study the existence and stability of the steady states. Then, we show that under some suitable conditions, both the malaria single infection model and co-infection model exhibit backward bifurcation. Furthermore, we analyze the conditions of extinction, competitive exclusion and co-existence of these two diseases. In addition, a local sensitivity analysis of the basic reproduction numbers is performed to explore the impact of the different parameters' variability on the dynamics of each disease. Moreover, we apply Pontryagin's maximum principle to determine optimal strategies to control the two diseases in case of co-infection. Finally, some numerical simulation results are presented to support the theoretical findings.

The global dynamic behavior of the respiration process in bacterial culture at different concentrations was comprehensively described using the qualitative theory of differential equations and symbolic calculation software.

This paper examines a three-species ecological competition model with two predators and one prey, incorporating food-limited growth and both linear and quadratic harvesting strategies. Using mathematical analysis, we identify equilibrium points and derive conditions for their stability and persistence. The results reveal that quadratic harvesting significantly enhances stability, promotes coexistence, and mitigates extinction risks compared to linear harvesting. Numerical simulations validate the theoretical findings, highlighting the effectiveness of quadratic harvesting in managing population dynamics. These insights contribute to the mathematical understanding of sustainable harvesting strategies in complex ecological systems.