Journal of Biological Dynamics最新文献

We investigate a mosquito population suppression model, which includes the release of Wolbachia-infected males causing incomplete cytoplasmic incompatibility (CI). The model consists of two sub-equations by considering the density-dependent birth rate of wild mosquitoes. By assuming the release waiting period T is larger than the sexual lifespan $\overline{T}$ of Wolbachia-infected males, we derive four thresholds: the CI intensity threshold $s_h^{\ast }$, the release amount thresholds $g^{\ast }$ and $c^{\ast }$, and the waiting period threshold $T^{\ast }$. From a biological view, we assume $s_h>s_h^{\ast }$ throughout the paper. When $g^{\ast }<c<c^{\ast }$, we prove the origin $E_0$ is locally asymptotically stable iff $T<T^{\ast }$, and the model admits a unique T-periodic solution iff $T\ge T^{\ast }$, which is globally asymptotically stable. When $c\ge c^{\ast }$, we show the origin $E_0$ is globally asymptotically stable iff $T\le T^{\ast }$, and the model has a unique T-periodic solution iff $T>T^{\ast }$, which is globally asymptotically stable. Our theoretical results are confirmed by numerical simulations.

In this paper, the invasive speed selection of the monostable travelling wave for a three-component lattice Lotka-Volterra competition system is studied via the upper and lower solution method, as well as the comparison principle. By constructing several special upper and lower solutions, we establish sufficient conditions such that the linear or nonlinear selection is realized.

The goal of this paper is to investigate the influence of the waning immunity on the dynamics of Tilapia Lake Virus (TiLV) transmission in wild and farmed tilapia within freshwater. We formulate a model for which susceptible individuals can contract the disease in two ways: (i) direct mode caused by contact with infected individuals; (ii) indirect mode due to the presence of pathogenic agents in the water. We obtain an age-structured model which combines both age since infection and age since recovery. We derive an explicit formula for the reproductive number $R_0$ and show that the disease-free equilibrium is locally asymptotically stable when, $R_0<1$. We discuss on the form of the waning immunity parameter and show numerically that a Hopf bifurcation may occur for suitable immunity parameter values, which means that there is a periodic solution around the endemic equilibrium when, $R_0>1$.

The novel Coronavirus (COVID-19) infection has become a global public health issue, and it has been a cause for morbidity and mortality of more people throughout the world. In this paper, we investigated the impacts of vaccination, other protection measures, home quarantine with treatment, and hospital quarantine with treatment strategies simultaneously using a deterministic mathematical modelling approach. No one has considered these intervention strategies simultaneously in his/her modelling approach. We examined all the qualitative properties of the model such as the positivity and boundedness of the model solutions, the disease-free and endemic equilibrium points, the effective reproduction number using next-generation matrix method, local stabilities of equilibrium points using the Routh-Hurwitz method. Using the Centre Manifold criteria, we have shown the existence of backward bifurcation whenever the COVID-19 effective reproduction number is less than unity. Moreover, we have analysed both sensitivity and numerical simulation using parameter values taken from published literature. The numerical results show that the transmission rate is the most sensitive parameter we have to control. Also vaccination, other protection measures, home quarantine with treatment, and hospital quarantine with treatment have great effects to minimize the COVID-19 transmission in the community.

We develop two discrete models to study how supplemental releases affect the Wolbachia spreading dynamics in cage mosquito populations. The first model focuses on the case when only infected males are released at each generation. This release strategy has been proved to be capable of speeding up the Wolbachia persistence by suppressing the compatible matings between uninfected individuals. The second model targets the case when only infected females are released at each generation. For both models, detailed model formulation, enumeration of the positive equilibria and their stability analysis are provided. Theoretical results show that the two models can generate bistable dynamics when there are three positive equilibrium points, semi-stable dynamics for the case of two positive equilibrium points. And when the positive equilibrium point is unique, it is globally asymptotically stable. Some numerical simulations are offered to get helpful implications on the design of the release strategy.

In this paper, we consider a fear effect predator-prey model with mutual interference or group defense. For the model with mutual interference, we show the interior equilibrium is globally stable, and the mutual interference can stabilize the predator-prey system. For the model with group defense, we discuss the singular dynamics around the origin and the occurrence of Hopf bifurcation, and find that there is a separatrix curve near the origin such that the orbits above which tend to the origin and the orbits below which tend to limit cycle or the interior equilibrium.

In this paper, we use a mean-reverting Ornstein-Uhlenbeck process to simulate the stochastic perturbations in the environment, and then a modified Leslie-Gower Holling-type II predator-prey stochastic model in a polluted environment with interspecific competition and pulse toxicant input is proposed. Through constructing V-function and applying $\mathrm{It}{\hat{o}}^{\text{'}}s$ formula, the sharp sufficient conditions including strongly persistent in the mean, persistent in the mean and extinction are established. In addition, the theoretical results are verified by numerical simulation.

This paper aims to analyse stability and Hopf bifurcation of the HIV-1 model with immune delay under the functional response of the Holling II type. The global stability analysis has been considered by Lyapunov-LaSalle theorem. And stability and the sufficient condition for the existence of Hopf Bifurcation of the infected equilibrium of the HIV-1 model with immune response are also studied. Some numerical simulations verify the above results. Finally, we propose a novel three dimension system to the future study.

Diabetes mellitus is a noncommunicable disease, which is a serious threat to human health around the world. In this paper, we propose a simple glucose-insulin model with Michaelis-Menten function as insulin degradation rate to mimic the pathogenic mechanism of diabetes. By theoretical analysis, a unique positive equilibrium of model exists and it is globally asymptotically stable. The four strategies are designed for diabetes patients based on the sensitivity of parameters, including insulin injection and medicine treatments. Numerical simulations are given to support the theoretical results.

This paper mainly explores the complex impacts of spatial heterogeneity, vector-bias effect, multiple strains, temperature-dependent extrinsic incubation period (EIP) and seasonality on malaria transmission. We propose a multi-strain malaria transmission model with diffusion and periodic delays and define the reproduction numbers $R_i$ and ${\hat{R}}_i$ (i = 1, 2). Quantitative analysis indicates that the disease-free ω-periodic solution is globally attractive when $R_i<1$, while if $R_i>1>R_j$ ($i\ne j,i,j=1,2$), then strain i persists and strain j dies out. More interestingly, when $R_1$ and $R_2$ are greater than 1, the competitive exclusion of the two strains also occurs. Additionally, in a heterogeneous environment, the coexistence conditions of the two strains are ${\hat{R}}_1>1$ and ${\hat{R}}_2>1$. Numerical simulations verify the analytical results and reveal that ignoring vector-bias effect or seasonality when studying malaria transmission will underestimate the risk of disease transmission.