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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]

A characteristic of ecosystems is the existence of manifold of independencies which are highly complex. Various mathematical models have made considerable contributions in gaining a better understanding of the predator–prey interactions. The main components of any predator–prey models are, firstly, how the different population classes grow and secondly, how the prey and predator interacts. In this paper, the two populations’ growth rates obey the logistic law and the carrying capacity of the predator depends on the available number of prey are considered. Our aim is to clarify the relationship between models and Holling types functional and numerical responses in order to gain insights into predator interferences and to answer an important question how competition is carried out. We consider a predator–prey model and a two-predator one-prey model to explain the idea. The novel approach is explained for the mechanism measurement of predator interference through depending on numerical response. Our approach gives good correspondence between an important real data and computer simulations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a predator–prey model with prey refuge and fear effect under non-diffusion and diffusion. For the non-diffusion ODE model, we first analyze the existence and stability of equilibria. Then, the existence of transcritical bifurcation, Hopf bifurcation and limit cycle is discussed, respectively. We find that when the cost of minimum fear η is taken as the bifurcation parameter, it not only influence the occurrence of Hopf bifurcation but also alters its direction. For diffusion predator–prey model under homogeneous Neumann boundary conditions, we observe that the Turing instability does not occur, but the Hopf bifurcation will manifest near the interior equilibrium. By considering η as the bifurcation parameter, the direction and stability of spatially homogeneous periodic orbits are established. At last, the validity of the theoretical analysis are verified by a series of numerical simulations. The results indicate that prey refuge and fear effect play an key role in the stability of populations. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a population suppression model and a population replacement model with periodic impulsive releases of Nilaparvata lugens infected with wStri. The conditions for the stability of wild- $ N.\,lugens $ N. l u g e n s -eradication periodic solution of two systems are obtained by applying the Floquet theorem and comparison theorem. And the sufficient conditions for the persistence in the mean of wild $ N.\,lugens $ N. l u g e n s are also given. In addition, the sufficient conditions for the extinction and persistence of the wild $ N.\,lugens $ N. l u g e n s in the subsystem without wLug are also obtained. Finally, we give numerical analysis which shows that increasing the release amount or decreasing the release period are beneficial for controlling the wild $ N.\,lugens $ N. l u g e n s , and the efficiency of population replacement strategy in controlling wild populations is higher than that of population suppression strategy under the same release conditions. [ABSTRACT FROM AUTHOR]

An intraguild predator–prey model including prey refuge and hunting cooperation is investigated in this paper. First, for the corresponding ordinary differential equation model, the existence and stability of all equilibria are given, and the existence of Hopf bifurcation, direction and stability of bifurcating periodic solutions are investigated. Then, for partial differential equation model, the diffusion-driven Turing instability is obtained. What is more, the existence and non-existence of the non-constant positive steady state of the reaction–diffusion model are established by the Leray–Schauder degree theory and some priori estimates. Next, some numerical simulations are performed to support analytical results. The results showed that prey refuge can change the stability of model and even have a stabilizing effect on this model, meanwhile the hunting cooperation can make such model without diffusion unstable, but make such model with diffusion stable. Lastly, a brief conclusion is concluded in the last section. [ABSTRACT FROM AUTHOR]

Predicting the evolution of expanding population is critical to control biological threats such as invasive species and virus explosion. In this paper, we consider a two species chemotaxis system of parabolic-parabolic-elliptic type with Lotka–Volterra type competition terms and a free boundary. Such a model with a free boundary describes the spreading of new or invasive species subject to the influence of some chemical substances in an environment with a free boundary representing the spreading front. We first find conditions on the parameters which guarantee the global existence and boundedness of classical solutions with nonnegative initial functions. Next, we investigate vanishing-spreading dichotomy scenarios for positive solutions. It is shown that the vanishing-spreading dichotomy in the generalized sense always occurs; that the vanishing spreading dichotomy in the strong sense occurs when the competition between two species is weak-weak competition; and that the vanishing spreading dichotomy in the weak sense occurs when the competition between two species is weak-strong competition. [ABSTRACT FROM AUTHOR]

In this paper, a generalized stochastic SIR epidemic model with vaccination rules is presented and the threshold behavior of the proposed epidemic model is investigated. Firstly, the stability of the equilibrium of the deterministic system is considered and the corresponding conditions are obtained. Secondly, the threshold of a stochastic SIR system for the extinction and the permanence in mean of epidemic disease are investigated. The results show that a larger stochastic disturbance can cause infections diseases to go to extinction. However, for a relatively small stochastic disturbance, the evolutionary dynamics of the epidemic diseases are overwhelmingly depend on the incidence function. This implies that the stochastic disturbance and the incidence function play an important role in diseases control. To test the theoretical results, a series of numerical simulations of these cases with respect to different noise disturbance coefficients are conducted. [ABSTRACT FROM AUTHOR]

In this paper, a six-neuron incommensurate fractional order BAM neural network model with multi-delays is considered. We demonstrate that the equilibrium point of the system loses its stability and Hopf bifurcation emerges when the delay passes through a critical value. And the relationship between the critical delay of Hopf bifurcation and size of fractional orders is found. Finally, some numerical simulations are given to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

The anthropogenic carbon dioxide (C O 2) emission from the burning of fossil fuels is the prime cause behind the menace of global warming. Over the past few decades, fossil fuel consumption has increased drastically to fulfill the energy demand of the growing population and economy. The population pressure has not only contributed to the increase in fossil fuel consumption but also accelerated the deforestation for industrial, agricultural, and infrastructure expansion. This paper presents a nonlinear mathematical model to study the effect of an increase in fossil fuel use and deforestation due to population pressure on atmospheric carbon dioxide concentration. Further, the effect of economic efforts applied to reduce the population pressure over the control of atmospheric C O 2 levels is explored. The model analysis shows that an increase in the fossil fuel consumption rate causes an increase in the equilibrium level of carbon dioxide. Further, it is found that an increase in the deforestation rate coefficient has a destabilizing effect on the stability of positive state of the system. If the deforestation rate crosses a critical threshold, the positive state of the system loses stability and the periodic solutions arise via Hopf-bifurcation. It is shown that at high deforestation rates, an increase in the implementation rate of economic efforts applied to reduce the population pressure may cause reduction in the amplitude of periodic oscillations. The periodic oscillations may disappear if the implementation rate of economic effort increased beyond a critical threshold and the concentration of carbon dioxide gets stabilized. [ABSTRACT FROM AUTHOR]

Malaria is preventable and curable but critical disease caused by parasites that are transmitted to people through the bites of female Anopheles mosquitoes. There were an estimated 228 million cases of malaria globally and its mortality remained at 405,000 in 2018. There are many models that have been developed but the aim of this paper is to analyse the potential impact of multiple current interventions in communities with limited resources. The authors in their previous work, developed a population-based model of malaria transmission dynamics to investigate the effectiveness of five different interventions. This model captured both the human and the mosquito compartments and considered 5 control interventions. Namely it was: educational campaigns to mobilise people for diagnostic test and treatment and to sleep under bed nets; treatment through mass drug administration; indoor residual spraying with insecticide to reduce malaria transmission; insecticide treated net to reduce morbidity; and regular destruction of mosquito breeding sites to reduce the number of new mosquito and bites/contact at dusks and dawn. In the present work we carried out basic mathematical analysis of the model, simulate the different scenarios developed and optimise the control interventions with optimal control. The potential of the control interventions to reduce transmission within 120 days was observed. The numerical experiments showed that the optimal strategy to effectively control malaria was through the combinations of controls in the models. The developed malaria model predicted the reduction, control and/or elimination of malaria threats through incorporating multiple control interventions. Therefore, multiple control measures should be adopted for malaria but in areas of limited resources, we can make use of strategy E and others in places where there are more resources. [ABSTRACT FROM AUTHOR]

A stock-effort dynamical model of a fishery with spatial structure is considered to assess the impacts of reserve size on fishing catch. We study the existence, uniqueness and global character of the solutions. It is shown that when the cost of fishing effort is less than the principal eigenvalue for an elliptic operator defined on a bounded domain corresponding to the fishing zone, then the fishery is viable, while in the opposite case, the fishery is not viable and fishing effort disappears. For both cases, the existence of stable solutions is studied. We perform some numerical simulations to illustrate our results in this paper and give a brief concluding remark. [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]

The bacterium E. coli is widely used to produce recombinant proteins such as growth hormone and insulin. One inconvenience with E. coli cultures is the secretion of acetate through overflow metabolism. Acetate inhibits cell growth and represents a carbon diversion, which results in several negative effects on protein production. One way to overcome this problem is the use of a synthetic consortium of two different E. coli strains, one producing recombinant proteins and one reducing the acetate concentration. In this paper, we study a mathematical model of such a synthetic community in a chemostat where both strains are allowed to produce recombinant proteins. We give necessary and sufficient conditions for the existence of a coexistence equilibrium and show that it is unique. Based on this equilibrium, we define a multi-objective optimization problem for the maximization of two important bioprocess performance metrics, process yield and productivity. Solving numerically this problem, we find the best available trade-offs between the metrics. Under optimal operation of the mixed community, both strains must produce the protein of interest, and not only one (distribution instead of division of labor). Moreover, in this regime acetate secretion by one strain is necessary for the survival of the other (syntrophy). The results thus illustrate how complex multi-level dynamics shape the optimal production of recombinant proteins by synthetic microbial consortia. [ABSTRACT FROM AUTHOR]

Epidemic diseases and media campaigns are closely associated with each other. Considering most epidemics have multiple pathogenic strains, in this paper, we take the lead in proposing two multi-strain SIS epidemic models in heterogeneous networks incorporating awareness programs due to media. For the first model, we assume that the transmission rates for strain 1 and strain 2 depend on the level of awareness campaigns. For the second one, we further suppose that awareness divides susceptible population into two different subclasses. After defining the basic reproductive numbers for the whole model and each strain, we obtain the analytical conditions that determine the extinction, coexistence and absolute dominance of two strains. Moreover, we also formulate its optimal control problem and identify an optimal implementation pair of awareness campaigns using optimal control theory. Given the complexity of the second model, we use the numerical simulations to visualize its different types of dynamical behaviors. Through theoretical and numerical analysis of these two models, we discover some new phenomena. For example, during the persistence analysis of the first model, we find that the characteristic polynomials of two boundary equilibria may have a pair of pure imaginary roots, implying that Hopf bifurcation and periodic solutions may appear. Most strikingly, multistability occurs in the second model and the growth rate of awareness programs (triggered by the infection prevalence) has a multistage impact on the final size of two strains. The numerical results suggest that the spread of a two-strain epidemic can be controlled (even be eradicated) by taking the measures of enhancing awareness transmission, reducing memory fading of aware individuals and ensuring high-level influx and rapid growth of awareness programs appropriately. [ABSTRACT FROM AUTHOR]

This paper investigates the stochastic dynamics of trophic cascade chemostat model perturbed by regime switching, Gaussian white noise and impulsive toxicant input. For the system with only white noise interference, sufficient conditions for stochastically ultimate boundedness and stochastically permanence are obtained, and we demonstrate that the stochastic system has at least one nontrivial positive periodic solution. For the system with Markov regime switching, sufficient conditions for extinction of the microorganisms are established. Then we prove the system is ergodic and has a stationary distribution. The results show that both impulsive toxins input and stochastic noise have great effects on the survival and extinction of the microorganisms. Finally, a series of numerical simulations are presented to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]