Journal of Biological Dynamics最新文献

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.

This paper is concerned with a stochastic SEIR model with infectivity in the incubation period and homestead-isolation on the susceptible, which is perturbed by white and colour noises. The model has a unique stationary distribution, which reflects the persistence of epidemics over a long period. Using the Has-minskii theorem and constructing stochastic Lyapunov functions with regime switching, we derive an important condition $R_0^s.$ Comparing the expression for $R_0$ and $R_0^s,$ we can see that if there is no environmental noise, then $R_0^s=R_0.$ It ensures the asymptotic stability of the positive equilibrium $E^{\ast }$ of the corresponding deterministic system.

The fear preoften leads to changes in the physiological characteristics of the prey. Different stages of prey exhibit different physiological behaviours, such as susceptibility to predator risk, which often leads to Allee effect. Taking into account the influence of these factors, a modified Leslie-Gower predator-prey model with Allee effect and stage structure is constructed in this paper. By use of variational technique and normal form theory, the criteria assuring the appearance of transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and its direction are all established. Specially, such codimension 2 bifurcations as Bautin bifurcation and Bogdanov-Takens bifurcation are presented. The bubble phenomenon and bistability are detected. All theoretical findings are verified by numerical examples. The biological effects of fear level, Allee effect and stage structure on system stability are analysed.

Measles is a highly contagious and potentially fatal disease, despite the availability of effective immunizations. This study formulates a deterministic mathematical model to investigate the transmission dynamics of measles, with eight compartments representing different epidemiological states such as susceptible, vaccinated, exposed, infected, early-treated, delayed-treated, hospitalized, and recovered individuals. We use the Next Generation Matrix (NGN) approach to obtain the basic reproduction number ($R_0$) and examine local stability at the disease-free equilibrium (DFE). Sensitivity analysis with Partial Rank Correlation Coefficients (PRCC) identifies significant parameters influencing disease dynamics, such as vaccination rates, transmission rate, treatment timings, and disease-induced mortality rates. Simulation results show that delayed therapy has a limited effect on lowering the infected population, emphasizing the importance of immediate intervention. Early treatment considerably reduces the number of infected individuals, whereas improved recovery rates in hospitalized cases result in fewer hospitalizations. Vaccination is extremely successful, with increased rates significantly lowering the susceptible population while boosting the vaccinated population. Higher disease-related mortality rates reduce the afflicted population, stressing the importance of strong control methods. The transmission rate has a substantial impact on infection rates and hospitalizations, emphasizing the need for effective public health policies and healthcare capacity. The combined effect of immunization and early treatment provides useful information for optimizing control measures. This study emphasizes the need of quick and effective measures in managing measles outbreaks and serves as a platform for future research into improved public health methods.

This article proposes a dispersal strategy for infected individuals in a spatial susceptible-infected-susceptible (SIS) epidemic model. The presence of spatial heterogeneity and the movement of individuals play crucial roles in determining the persistence and eradication of infectious diseases. To capture these dynamics, we introduce a moving strategy called risk-induced dispersal (RID) for infected individuals in a continuous-time patch model of the SIS epidemic. First, we establish a continuous-time n-patch model and verify that the RID strategy is an effective approach for attaining a disease-free state. This is substantiated through simulations conducted on 7-patch models and analytical results derived from 2-patch models. Second, we extend our analysis by adapting the patch model into a diffusive epidemic model. This extension allows us to explore further the impact of the RID movement strategy on disease transmission and control. We validate our results through simulations, which provide the effects of the RID dispersal strategy.

In this paper, we consider a stochastic two-species predator-prey system with modified Leslie-Gower. Meanwhile, we assume that hunting cooperation occurs in the predators. By using Itô formula and constructing a proper Lyapunov function, we first show that there is a unique global positive solution for any given positive initial value. Furthermore, based on Chebyshev inequality, the stochastic ultimate boundedness and stochastic permanence are discussed. Then, under some conditions, we prove the persistence in mean and extinction of system. Finally, we verify our results by numerical simulations.

In this paper, a compartmental model on the co-infection of pneumonia and HIV/AIDS with optimal control strategies was formulated using the system of ordinary differential equations. Using qualitative methods, we have analysed the mono-infection and HIV/AIDS and pneumonia co-infection models. We have computed effective reproduction numbers by applying the next-generation matrix method, applying Castillo Chavez criteria the models disease-free equilibrium points global stabilities were shown, while we have used the Centre manifold criteria to determine that the pneumonia infection and pneumonia and HIV/AIDS co-infection exhibit the phenomenon of backward bifurcation whenever the corresponding effective reproduction number is less than unity. We carried out the numerical simulations to investigate the behaviour of the co-infection model solutions. Furthermore, we have investigated various optimal control strategies to predict the best control strategy to minimize and possibly to eradicate the HIV/AIDS and pneumonia co-infection from the community.