Journal of Biological Dynamics最新文献

This paper proposes an immunosuppressive infection model with time delay and stochastic perturbation. A stochastic threshold $R_0^s$ is constructed, and the sufficient conditions for virus extinction and weak persistence are given. Subsequently, we respectively fit the SDDE and ODE models to the real data, and conduct a sensitivity analysis of the equilibrium. The greater the noise intensity, the more obvious the oscillation amplitude of the solution curve around the immune-free equilibrium, the larger noise intensity can cause the originally persistent virus in ODE to go extinct in the SDDE model. The greater the time delay, the longer it takes for the virus and immune cells to reach their first peaks. The viral replication rate significantly affects the virus-immune system, and the reproduction of HIV-1 can be inhibited by modulating it. A relatively high viral inhibition rate will lead to the extinction of immune cells while the virus persists.

Chemical control is crucial in pest management, but delayed responses to pesticide application can significantly affect its success. This study develops a type of novel mathematical models combining delayed impulse differential equations with pulse pesticide spraying to evaluate these delayed effects. The uniform stability of the pest eradication solution is analysed, and key parameters influencing pest control success are explored. Considering delays in both pest population growth reaching environmental capacity and pesticide response, a double delayed impulse differential equation is formulated. The asymptotic stability and exponential stability of the system are studied, and threshold conditions for pest extinction are identified. The findings help optimize pest control strategies under delayed pesticide responses.

Human papillomavirus (HPV) infection is the most common sexually transmitted infection in the world. Persistent oncogenic HPV infection has been a leading threat to global health and can lead to serious complications such as cervical cancer. Prevention interventions including vaccination and screening have been proven effective in reducing the risk of HPV-related diseases. In recent decades, computational epidemiology has been serving as a very useful tool to study HPV transmission dynamics and evaluation of prevention strategies. In this paper, we conduct a comprehensive literature review on state-of-the-art computational epidemic models for HPV disease dynamics, transmission dynamics, as well as prevention efforts. Selecting 45 most-relevant papers from an initial pool of 10,497 papers identified through keyword search, we classify them based on models used and prevention strategies employed, summarize current research trends, identify gaps in the present literature, and identify future research directions. In particular, we describe current consensus regarding optimal prevention strategies which favour prioritizing teenage girls for vaccination. We also note that optimal prevention strategies depend on the resources available in each country, with hybrid vaccination and screening being the most fruitful for developed countries, and screening-only approaches being most cost effective for low and middle income countries. We also highlight that in future, the use of computational and operations research tools such as game theory and linear programming, coupled with the large scale use of census and geographic information systems data, will greatly aid in the modelling, analysis and prevention of HPV.

Heterogeneity of population is a key factor in modelling the transmission of disease among the population and has huge impact on the outcome of the transmission. In order to investigate the decision-making process in the heterogeneous mixing population regarding whether to be vaccinated or not, we propose the modelling framework which includes the epidemic models and the game theoretical analysis. We consider two sources of heterogeneity in this paper: the different activity levels and the different relative vaccination costs. It is interesting to observe that, if both sources of heterogeneity are considered, there exist a finite number of Nash equilibria for the vaccination game. While if only the difference of activity levels is considered, there are infinitely many Nash equilibria. For the latter case, the initial condition of the decision-making process becomes highly sensitive. In the application of public health management, the inclusion of population heterogeneity significantly complicates the prediction of the overall vaccine coverage level in the whole population.

We use mathematical modeling to study the proliferation dynamics of CD4+ T cells within an immune response. This proliferation is driven by the autocrine reaction of helper T cells and interleukin-2 (IL-2), and regulated by natural regulatory T cells (nTregs). Previous studies suggested that a fratricidal mechanism is necessary to eliminate helper T cells post-infection. Contrary to this, our mathematical analysis establishes that the depletion of these cells is due to two pivotal factors: the saturation in the proliferation rate of helper CD4+ T cells at high IL-2 concentrations, and the activation rate of nTregs outpacing their death rate. This yields an excitable process, such that the proliferation starts once the helper T cell population passes a threshold. Additionally, we find that when the proliferation of nTregs lags behind their mortality, induced regulatory T cells (iTregs) are crucial to curbing the proliferation of helper CD4+ T cells.

Macrophages have both anti-tumor and pro-tumor effects. Time delay is commonly observed in real systems, yet its impact on tumor-macrophage dynamics remains unclear. This paper develops a new tumor-macrophage model with time delay. The model describes the interactions between tumor cells (T), the classically activated macrophages (M1), the alternatively activated macrophages (M2), and the inactive macrophages (M0). The system's solution is computed, and equilibrium stability is analyzed. The existence of Hopf bifurcation is subsequently established. There exists bifurcating periodic solutions near the internal equilibrium, showing tumor cells and macrophages can coexist in the long term, as well as the potential for tumor relapse. Furthermore, the normal form and center manifold theorem are utilized to study the nature of Hopf bifurcation. Sensitivity analysis highlights the effect of parameters on tumor population dynamics. Numerical simulations validate the theory, elaborating the model can serve as a useful tool for tumor system analysis.

The Ricker-type growth model, which incorporates a density-dependent mechanism, is widely used in ecological modelling to fit a broad range of complex population growth patterns. In this study, the complex dynamics of a modified Hassell-Varley model with Ricker growth were analysed. We first investigated the permanence of solutions, the existence and uniqueness of the positive steady state and the local stability of equilibrium points. We confirm that, under certain parametric conditions, the proposed system undergoes a flip or Neimark-Sacker bifurcation within the interior of $R_{+}^2$. Two feedback control measures were employed to control bifurcation and chaos in the proposed system. Simultaneously, several examples are provided to support our theoretical results using numerical simulations, and are conducted to illustrate the intricate behaviours of the modified Hassell-Varley model.

In this paper, we study the dynamics of a delayed predator-prey model with harvesting and prey refuge. For the model without time delays, we show the stability of boundary and positive equilibria, given the existence of bionomic equilibrium, and provide the optimal harvesting policy. For the model with time delays, we show the local stability of the positive equilibrium for four different time delay cases, give the existence of Hopf bifurcation near the positive equilibrium, and prove the direction and stability of bifurcating periodic solutions. Ecologically, via numerical simulations, we find that the synergistic effects of time delay, refuge and harvesting can have complex effects on population dynamics. One of the most important results indicates that the increase of prey refuge or prey harvesting rate can eliminate the periodic solutions induced by time delay, while the increase in predator harvesting rate can maintain this periodic phenomenon.

This paper formulates a mathematical model for the co-infection of HTLV-2 and HIV-1 with latent reservoirs, four types of distributed-time delays and HIV-1-specific B cells. We establish that the solutions remain bounded and nonnegative, identify the system's steady states, and derive sufficient conditions ensuring both their existence and global asymptotic stability. The system's global stability is confirmed using Lyapunov's method. We provide numerical simulations to support the stability results. Sensitivity analysis of basic reproduction numbers of HTLV-2 mono-infection ($R_1$) and HIV-1 mono-infection ($R_2$) is conducted. We examine how time delays influence the interaction between HIV-1 and HTLV-2. Including delay terms in the model reflects the influence of antiviral treatments, which help decrease $R_1$ and $R_2$, thus limiting the spread of infection. This highlights the potential for designing therapies that prolong delay period. Incorporating such delays improves model precision and supports more effective evaluation of treatment strategies.

Integrated pest management (IPM) combines chemical and biological control to maintain pest populations below economic thresholds. The impact of providing additional food for predators on pest-predator dynamics, along- side pesticide use, in the IPM context remains unstudied. To address this issue, in this work a theoretical model was developed using differential equations, assuming Holling type II functional response for the predator, with additional food sources included. Strategies for controlling pest populations were derived by analyzing Hopf bifurcation occurring in the system using dynamical system theory. The study revealed that the quality and quantity of additional food supplied to predators play a crucial role in the system's dynamics. Pesticides, combined with the introduction of predators supported by high-quality supplementary food, enable a quick elimination of pests from the system more effectively. This observation highlights the role of IPM in optimizing pest management strategies with minimal pesticide application and supporting the environment.