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This paper studies an impact of media epidemic system with diffusion and linear source. We first derive the uniform bounds of solutions to impact on media reaction diffusion system. Then, the basic reproduction number is calculated and the threshold dynamics of impact media reaction diffusion system is also given and the Kuratowski measure κ of non-compactness is also considered. In addition, assume the spatial environment is homogeneous, it is shown that the unique endemic equilibrium of the system is global stability by constructing suitable Lyapunov function. Finally, we discuss the asymptotic profile of the system when the diffusion rate of the susceptible (infected) individuals for the system tends to zero or infinity. The main results show that the activities of infected individuals can only be at low risk, and then the virus eventually will be extinct, that is, to control the entry of viruses from abroad and increase the detection of domestic viruses. Finally, some numerical simulations are worked out to confirm the results obtained in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the spreading behavior of a two-species strong-weak competition system with two free boundaries. The model may describe how a strong competing species invades into the habitat of a native weak competing species. The asymptotic spreading speed of invading fronts has been determined by making use of semi-wave systems in Du et al. (J Math Pures Appl 107:253–287, 2017). Here we give a sharp estimate for the asymptotic spreading speed of invading fronts. Moreover, we prove that the solution of the free boundary problem evolves eventually into a semi-wave solution when the spreading happens, while the solution of the free boundary problem exponentially converges to a semi-trivial solution of such system when the vanishing happens. [ABSTRACT FROM AUTHOR]

In this paper, we incorporate stoichiometry into a competition model in chemostat culture. We first discuss the dynamics of this stoichiometric chemostat model for single algae species. We obtain the uniform persistence and find that an increase of phosphorus input or a slow dilution rate facilitates the algal persistence. Then, we consider a stoichiometric chemostat model in which two species competing for single nutrient, investigate how stoichiometry, dilution rate and concentration of phosphorus input affect the result of competition between algae species. Competitive exclusion and coexistence of two competing algae species are explored by discussing the existence, local stability of all feasible equilibria. Previous studies suggested that competitive exclusion holds in general chemostat models with two species competing for one limiting nutrient. Our theoretical and numerical results demonstrate that stoichiometry brings the coexistence of two competing algae species. Moreover, under low phosphorus input or fast dilution rate, competitive exclusion still holds. High phosphorus input or slow dilution rate facilitates the coexistence of multiple species. [ABSTRACT FROM AUTHOR]

In control of wild mosquitoes to fight mosquito-borne diseases, release of mosquitoes with Wolbachia is one of the effective biological control methods. There are three release strategies, namely releasing both Wolbachia-infected females and males, only Wolbachia-infected females and only Wolbachia-infected males. All these three strategies have been confirmed to be capable of speeding up the Wolbachia persistence in mosquito populations. In this paper, we investigate how supplementary releases affect the Wolbachia spread dynamics in mosquito populations. Our aim is to compare the effectiveness among these three release strategies. We obtain theoretical results and provide numerical simulations that show that the first two strategies are more effective than the last strategy. For the first two strategies, the former strategy is either less effective than the latter strategy in each generation, or more effective than the latter strategy in previous generations, and then becomes less effective in late generations. [ABSTRACT FROM AUTHOR]

Phylogenetic diversity indices provide a formal way to apportion evolutionary history amongst living species. Understanding the properties of these measures is key to determining their applicability in conservation biology settings. In this work, we investigate some questions posed in a recent paper by Fischer et al. (Syst Biol 72(3):606–615, 2023). In that paper, it is shown that under certain extinction scenarios, the ranking of the surviving species by their Fair Proportion index scores may be the complete reverse of their ranking beforehand. Our main results here show that this behaviour extends to a large class of phylogenetic diversity indices, including the Equal-Splits index. We also provide a necessary condition for reversals of Fair Proportion rankings to occur on phylogenetic trees whose edge lengths obey the ultrametric constraint. Specific examples of rooted phylogenetic trees displaying these behaviours are given and the impact of our results on the use of phylogenetic diversity indices more generally is discussed. [ABSTRACT FROM AUTHOR]

We consider the long-time behaviour of a West Nile virus (WNv) model consisting of a reaction–diffusion system with free boundaries. Such a model describes the spreading of WNv with the free boundary representing the expanding front of the infected region, which is a time-dependent interval $[g(t), h(t)]$ in the model (Lin and Zhu, Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary. J. Math. Biol. 75, 1381–1409, 2017). The asymptotic spreading speed of the front has been determined in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019) by making use of the associated semi-wave solution, namely $\lim _{t\to \infty } h(t)/t=\lim _{t\to \infty }[\!-g(t)/t]=c_\nu$ , with $c_\nu$ the speed of the semi-wave solution. In this paper, by employing new techniques, we significantly improve the estimate in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019): we show that $h(t)-c_\nu t$ and $g(t)+c_\nu t$ converge to some constants as $t\to \infty$ , and the solution of the model converges to the semi-wave solution. The results also apply to a wide class of analogous Ross–MacDonold epidemic models. [ABSTRACT FROM AUTHOR]

This paper considers a density-suppressed motility model with a strong Allee effect under the homogeneous Neumman boundary condition. We first establish the global existence of bounded classical solutions to a parabolic–parabolic system over an |$N $| -dimensional |$\mathbf{(N\le 3)}$| bounded domain |$\varOmega $|⁠ , as well as the global existence of bounded classical solutions to a parabolic–elliptic system over the multidimensional bounded domain |$\varOmega $| with smooth boundary. We then investigate the linear stability at the positive equilibria for the full parabolic case and parabolic–elliptic case, respectively, and find the influence of Allee effect on the local stability of the equilibria. By treating the Allee effect as a bifurcation parameter, we focus on the one-dimensional stationary problem and obtain the existence of non-constant positive steady states, which corresponds to small perturbations from the constant equilibrium |$(1,1)$|⁠. Furthermore, we present some properties through theoretical analysis on pitchfork type and turning direction of the local bifurcations. The stability results provide a stable wave mode selection mechanism for the model considered in this paper. Finally, numerical simulations are performed to demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

Temperature-dependent sex determination (TSD) is an environmental phenomenon in which the temperature during the embryonic or larval stages influences the determination of sex. It is mainly observed in teleost fish, where high water temperatures can induce a female-to-male transition. The exact mechanism by which environmental changes affect TSD is poorly understood, but cortisol, a stress hormone, is considered a potential factor. Although excessive secretion of cortisol is known to cause side effects, it can lead to a switch in sex hormones, potentially resulting in TSD. In this paper, we investigate the mechanism of TSD in teleost fish. To assess the impact of stress caused by changes in water temperature on TSD, we established a mathematical model for hormonal dynamics that incorporates cortisol. First, we conducted a stability analysis to qualitatively examine the sex determination. The temperature dependence was modeled using the Eyring–Polanyi equation, and we examined corresponding hormonal changes with water temperature. Furthermore, we theoretically investigated the role of a cortisol inhibitor in preventing side effects during TSD. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the dynamic behavior of a novel stochastic epidemic model (SEM) that incorporates distributed delay and time switching. We prove the existence and uniqueness of a global positive solution and establish the presence of ergodic stationary distribution (ESD) through the construction of appropriate Lyapunov functions. The threshold R 0 S derived from our analysis plays a vital role in this procedure. Additionally, we conduct computer simulations to validate our theoretical discoveries, demonstrating that the incorporation of white noise can induce random fluctuations in the system variables under time switching. [ABSTRACT FROM AUTHOR]

In this paper, we establish a discrete model with periodic parameters to depict the Wolbachia spread dynamics in mosquito populations in cyclic environments. This work modifies the models established in the existing literature that did not take into account the variation of parameters with environmental periodic changes due to seasonality and other factors. When the parameters in our model are constants, it has been extensively studied and widely used. We present a conjecture about the existence of at most two periodic solutions worthy of further study, and show that the conjecture is true for the special case of 2-periodic parameters. Numerical simulations are also provided to illustrate the occurrence of periodic phenomena. [ABSTRACT FROM AUTHOR]

To describe the transmission dynamics of maize streak virus infection, in the paper, we first formulate a stochastic maize streak virus infection model, in which the stochastic fluctuations are depicted by a logarithmic Ornstein–Uhlenbeck process. This approach is reasonable to simulate the random impacts of main parameters both from the biological significance and the mathematical perspective. Then we investigate the detailed dynamics of the stochastic system, including the existence and uniqueness of the global solution, the existence of a stationary distribution, the exponential extinction of the infected maize and infected leafhopper vector. Especially, by solving the five-dimensional algebraic equations corresponding to the stochastic system, we obtain the specific expression of the probability density function near the quasi-endemic equilibrium of the stochastic system, which provides valuable insights into the stationary distribution. Finally, the model is discretized using the Milstein higher-order numerical method to illustrate our theoretical results numerically. Our findings provide a groundwork for better methods of preventing the spread of this type of virus. [ABSTRACT FROM AUTHOR]

In this paper, we consider a multigroup stochastic SIQR epidemic model with varying total population size. After proving the existence and uniqueness of the global solution to the system, we developed sufficient conditions for the existence of an stationary ergodic distribution of the positive solutions. Then we gave sufficient conditions for extinction of the diseases which is based on the basic reproduction number in its corresponding deterministic system. [ABSTRACT FROM AUTHOR]

In the study of biological populations, the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction. This effect supersedes the classical logistic model, in which low densities are favorable due to lack of competition, and includes situations related to deficit of genetic pools, inbreeding depression, mate limitations, unavailability of collaborative strategies due to lack of conspecifics, etc. The goal of this paper is to provide a detailed mathematical analysis of the Allee effect. After recalling the ordinary differential equation related to the Allee effect, we will consider the situation of a diffusive population. The dispersal of this population is quite general and can include the classical Brownian motion, as well as a Lévy flight pattern, and also a “mixed” situation in which some individuals perform classical random walks and others adopt Lévy flights (which is also a case observed in nature). We study the existence and nonexistence of stationary solutions, which are an indication of the survival chance of a population at the equilibrium. We also analyze the associated evolution problem, in view of monotonicity in time of the total population, energy consideration, and long-time asymptotics. Furthermore, we also consider the case of an “inverse” Allee effect, in which low density populations may access additional benefits. [ABSTRACT FROM AUTHOR]

In this paper, assuming the certain variable satisfies the Ornstein–Uhlenbeck process, we formulate a stochastic within-host dengue model with immune response to obtain further understanding of the transmission dynamics of dengue fever. Then we analyze the dynamical properties of the stochastic system in detail, including the existence and uniqueness of the global solution, the existence of a stationary distribution, and the extinction of infected monocytes and free viruses. In particular, it is worth revealing that we get the specific form of covariance matrix in its probability density around the quasi-endemic equilibrium of the stochastic system. Finally, numerical illustrative examples are depicted to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

Pyrethroid-treated bed-nets (PTNs) protect individuals against malaria by blocking and repelling mosquitoes. We develop and analyze a PTNs malaria model that explicitly includes mosquito host choice (also known as feeding/biting preference) and Pyrethroid repellent effect. Our model reveals that mosquito biting/feeding preference on infectious hosts π and repellent effect r drive for the existence of both the endemic equilibrium points and the occurrence or elimination of backward bifurcation. The threshold parameters for the mosquito biting preference on infectious hosts π ∗ and repellent effect r ∗ for the occurrence and elimination of backward bifurcation are computed. Moreover, it is shown that, increasing the mosquito host choice rate or decreasing the repellent effect rate, annihilates backward bifurcation, thus facilitating the control of malaria. Furthermore, we prove that the threshold of mosquito biting preference is a monotone increasing function of the repellent effect r. We show that the model exhibits both trans-critical forward bifurcation and backward bifurcation when either the mosquito host choice π crosses a threshold value π 1 or the repellent effect r passes through a threshold repellent rate r 1 . Sufficient conditions for the global asymptotic stability of the equilibrium point are derived. On the other hand, it is established that, decreasing the mosquito biting preference or increasing the rate of the repellent effect (i.e personal protection) or the combining both actions, decreases the malaria control reproduction number R 0 . Finally, the interplay between the bed-nets treated repellent effect and mosquito host choice and its potential on the dynamics of malaria is investigated and illustrated numerically. [ABSTRACT FROM AUTHOR]

Zebra mussels have caused significant damage in many lakes and rivers. By using a hybrid population model with discrete-time equations and ordinary differential equations, we represent the zebra mussel's life cycle, growth, and population movement. The dynamics of the larvae (unsettled and settled larvae) are represented during the summer months in a system of two ordinary differential equations, while the juvenile, small adult, and large adult stages are represented by a discrete model with yearly time steps. The goal is to investigate the effects of zebra mussel movement between three different spatial locations and possible control measures. Zebra mussel data and temperature values from three locations in the Hudson River over several years were used to estimate model parameters. We investigate the stability and net reproductive number for our model. We illustrate numerically the hybrid population model for several scenarios of movement and cleaning boats to remove mussels. [ABSTRACT FROM AUTHOR]

Vaccination and social media play pivotal roles in affecting disease transmission. Research has shown that disease transmission can be subject to random events. Consequently, we develop a stochastic infectious disease dynamical model that incorporates saturated media coverage and vaccination age. The Itô's formula and the Lyapunov function method are applied to study the extinction behavior of the disease and the existence of a unique ergodic stationary distribution. The findings suggest that the media effect is delayed and cannot eliminate the disease completely. To directly control disease transmission, a combination of high-intensity noise disturbance and low vaccine wane rate is required. Furthermore, the shorter the disease incubation period, the more difficult it is to control. [ABSTRACT FROM AUTHOR]