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This paper analyzes an allelopathic phytoplankton competition model, which was proposed by Bandyopadhyay [Dynamical analysis of a allelopathic phytoplankton model, J Biol Syst14(02):205–217, 2006]. Our study refines the previous results and finds at most three positive equilibria for the system. The existence conditions of all positive equilibria and the corresponding stability cases are given in the paper. Interesting dynamical phenomena such as bistability, saddle-node bifurcation, and cusp bifurcation are found. It is shown that the rate of toxin releases heavily influences the positive equilibria of the system under certain conditions. Numerical simulations verify the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a modified Lasslie–Gower-type predator–prey model with the effect of hunting cooperation and favorable additional food for predator. We establish the conditions of positivity, boundedness, and permanence of solutions of the proposed model. Along with the trivial, predator free, prey free equilibrium points the system contains at most two coexistence equilibrium points. The system experiences the transcritical, saddle-node, Hopf, cusp, Bautin, and Bogdanov–Takens bifurcation depending on the model parameters. All the theoretical analyses are verified using numerical simulations. It is numerically established that the cooperation and extra food have high impact on the model dynamics. [ABSTRACT FROM AUTHOR]

This paper studies the dynamics of a class of host-parasitoid models with host refuge and the strong Allee effect upon the host population. Without the parasitoid population, the Beverton–Holt equation governs the host population. The general probability function describes the portion of the hosts that are safe from parasitism. The existence and local behavior of solutions around the equilibrium points are discussed. We conclude that the extinction equilibrium will always have its basin of attraction which implies that the addition of the host refuge will not save populations from extinction. By taking the host intrinsic growth rate as the bifurcation parameter, the existence of the Neimark–Sacker bifurcation can be shown. Finally, we present numerical simulations to support our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we propose an epidemic model of SIR type with ratio-dependent impulse control and Beddington–DeAngelis (B–D) incidence. According to the magnitude of the basic reproductive number ℛ0 and the relation of the endemic equilibrium (S∗,I∗) and the ratio threshold h, dynamical analysis of the controlled system is conducted. Under the control strategy, if ℛ0 ≤ 1, the solutions converge to the disease-free equilibrium. If ℛ0 > 1 and I∗ S∗ > h, the impulsive system has periodic solution that is orbitally asymptotically stable, and order-k (k > 2) periodic solution does not exist. Furthermore, if ℛ0 > 1 and I∗ S∗ < h, the solution converges either to the endemic equilibrium or to a periodic solution, which is proved to be determined by the initial value. Finally, numerical simulations are performed to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a two-dimensional modified Leslie–Gower predator–prey model with carry-over effects, fear, prey protection and additional food, including prey harvesting. For this, it assumes the carry-over effect with delay incorporated in the birth rate of the prey population and gestation delay in Leslie–Gower term of a predator, and supposes that the predator consumes the prey according to Holling type II functional response. This dynamical system is split into two groups, namely non-delayed and delayed systems, respectively. In the non-delayed system, first, we discuss positivity, boundedness solutions, and the existence of equilibria, especially finding the coexistence of interior equilibrium points under certain conditions. After that, local and global stabilities are systematically analyzed. In addition, we obtain the conditions of Hopf-bifurcation in terms of the growth rate of prey species, prey protection and preference rate of predator for the non-delayed system. Whereas in the delayed system, both the delays have an essential role in governing the dynamical system discussed in three cases, and each case found the Hopf-bifurcation parameters for which the system changes stability behavior into instability. At last, the numerical simulations have been carried out to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

A mathematical model has been proposed to consider two distinct forms of psychological pressure that arise due to the COVID-19 situation and their impact on individuals' lives, including their mental well-being and happiness. For a more realistic situation, the effect of stochasticity should be taken into account. Hence, our paper mainly investigates the effect of stochastically environmental variability on the transmission dynamics of psychological stress. We obtain two thresholds ℛ s 1 and ℛ s 2 . If ℛ s 1 > 1 , the psychological stress will persist and there will be a unique stationary distribution; whereas if ℛ s 2 < 1 , the extinction of psychological stress is obtained. Moreover, we display the mean first passage time from the initial value to the state of disappearance in order to examine the impact of environmental disturbances; meanwhile, we conduct numerical simulations to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we consider a stochastic food chain chemostat model with variable yields. First, we prove the stochastic model has a unique global positive solution. Second, by employing suitable Lyapunov functions, Itô ′ s formula and some other important inequalities, the existence of a unique ergodic stationary distribution of a stochastic food chain chemostat model is researched, which can help us better understand the statistical characteristics of stochastic food chain chemostat models. Second, we investigate the extinction of the microorganism and the bacteria. Moreover, the case of extinction for bacteria but persistence for microbial species is considered. Finally, some numerical simulations are carried out to illustrate our theoretical results and the influence of the variable yields on the microorganism and the bacteria. [ABSTRACT FROM AUTHOR]

In this paper, a predator–prey model with prey refuge was developed to investigate how prey refuge affect the dynamics of predator–prey interaction. We studied the existence and stability of equilibria, and then derived the sufficient conditions for the bifurcation such as saddle-node, transcritical, Hopf and Bogdanov–Takens bifurcation. In addition, a series of numerical simulations were carried out to illustrate the theoretical analysis, and the numerical results are consistent with the analytical results. Our results demonstrate that prey refuge has a great impact on the predator–prey dynamics. [ABSTRACT FROM AUTHOR]

This paper considers predator–prey systems in which the predator adapts the search speed to prey's density. The prey admits the cost of fear because of the predator and moves between source–sink patches to escape from predation. Using dynamical systems theory, we demonstrate equilibrium stability, uniform persistence and bifurcations in the system. It is shown that enhancing the search speed of predator and/or decreasing prey's dispersal from the source to sink could promote persistence of the system, while increasing the fear cost would stabilize the system. Moreover, dispersal could make the prey persist in both source–sink patches, even drive the predator into extinction. The dispersal could also make the prey reach a total population abundance larger than that without dispersal, even larger than the carrying capacity. Asymmetry in dispersal plays a role in the persistence and abundance. A novel finding of this work is that dispersal may lead to results reversing those without dispersal. Numerical simulations illustrate and extend our results. This work is important in understanding complexity in predation systems. [ABSTRACT FROM AUTHOR]

In this paper, rich dynamics and complex bifurcations of an SIR epidemic model with saturated incidence rate and strong Allee effect are investigated. First, the existence of disease-free and endemic equilibria is explored, and we prove that the system has at most three positive equilibria, which exhibit different types such as hyperbolic saddle and node, degenerate unstable saddle (node) of codimension 2, degenerate saddle-node of codimension 3 at disease-free equilibria, and cusp, focus, and elliptic types Bogdanov–Takens singularities of codimension 3 at endemic equilibria. Second, bifurcation analysis at these equilibria are investigated, and it is found that the system undergoes a series of bifurcations, including transcritical, saddle node, Hopf, degenerate Hopf, homoclinic, cusp type Bogdanov–Takens of codimensional 2, and focus and elliptic type Bogdanov–Takens bifurcation of codimension 3 which are composed of some bifurcations with lower codimension. The system shows very rich dynamics such as the coexistence of multiple periodic orbits and homoclinic loops. Finally, numerical simulations are conducted on the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a discrete-time Ricker population model with the strong Allee effect is proposed, and its complex dynamic behavior is analyzed. First, the existence and asymptotic stability of the unique positive equilibrium are studied. Second, Neimark–Sacker and period-doubling bifurcations of this discrete model were carried out, and corresponding bifurcation conditions were obtained. Third, the pole placement method and the hybrid control strategy have been used to control the chaos produced by these bifurcations. Finally, we use MATLAB software to carry out some numerical simulations to analyze the rich dynamics of the system as well as to verify our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated global dynamics of a two-species food chain model with the Holling type III functional response that includes linear harvesting for the prey and nonlinear harvesting for the predator. The long-time continued existence of both species is discussed using uniform persistence theory. Stability of various equilibrium points is described in terms of model parameters. The local asymptotic stability of non-hyperbolic equilibrium points is determined with the help of center manifold theorem. Global behavior of solutions of the model system when both species are present is determined by considering the global properties of the coexistence equilibrium. Here, we have taken a comprehensive view by considering different bifurcations of co-dimension one and two and have discussed the importance of various model parameters on the system dynamics. The model system shows much more complex and realistic behavior compared to a model system without any harvesting, with constant harvesting or linear-yield harvesting of either or both of the species. Numerical simulations have been conducted to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a stochastic chemostat model with impulsive perturbation on the nutrient. First, the existence and uniqueness of solutions are proved by constructing a pulseless equivalent system. Second, based on Khasminskii's Markov periodic process theory, we give sufficient conditions for the existence of positive T -periodic solutions. Third, under certain conditions, the existence and global attractivity of boundary periodic solutions are established by using comparison theorem. Finally, numerical simulations are provided to verify our main results. [ABSTRACT FROM AUTHOR]

In this paper, we use the classical Ross–Macdonald model to analyze the effect of the Mosquito Home System (MHS), which is an example of an auto-dissemination trap, in controlling the spread of dengue in Malaysia in a high-rise condominium environment. By using the national dengue data from Malaysia, we are able to estimate ł which represents the initial growth rate of the dengue epidemic and thus allows us to estimate the number of mosquitoes in Malaysia. The basic reproduction number R 0 is also obtained. We have constructed a mathematical expression which allows us to estimate the potential number of breeding sites for Aedes mosquitoes. Later on, by using the data available from the 11 months trials carried out in three blocks of flats in Selangor, we improved on our dengue model by including the effect of the MHS and thus modeling the impact it has on the spread of dengue within the flats. Numerical simulations and tables are also produced to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper deals with problems of stability and travelling waves for a class of recurrent neural networks with arbitrary exponents k and m. A novel model which is not only nonlinear but also coupled is proposed. This paper makes the following contributions: (1) Conditions for local stablility of 1-D networks and 2-D networks are established with a series of mathematical arguments. (2) Completely convergence of 1-D neural networks is proved by constructing a suitable energy function. (3) The nonuniform solution of the networks is obtained when the connectivity is Gaussian profile. (4) Travelling waves of the networks are analyzed with the connectivity profile. Finally, simulation examples are employed to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting. [ABSTRACT FROM AUTHOR]

In this paper, a model of stochastic competition between plasmid-bearing and plasmid-free organisms in a chemostat is investigated. First, we show that there is a unique global positive solution for the stochastic system. Second, by employing stochastic Lyapunov functions, Itô formula, strong law of large number and some other important inequalities, stochastic characteristics of the stochastic competition chemostat model are studied such as the stochastic asymptotic behaviors of the system. Finally, some numerical simulations are given. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study the dynamical properties of a discrete-time prey–predator model under imprecise biological parameters. We consider refuge for prey species as a constant number. The equilibria of the model are obtained, and the dynamic behaviors of the proposed system are examined for the interval biological parameters. Simulations of the model are performed for different parameters of the model. Numerical simulations demonstrate that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature. [ABSTRACT FROM AUTHOR]

Spatial patterns through diffusion-driven instability are stationary structures that appear spontaneously upon breaking the symmetry of the spatial domain, which results only from the coupling between the reaction and the diffusion processes. This paper is concerned with a modified Leslie–Gower-type model with cross-diffusion and indirect predation effect. We first prove the global existence, non-negativity and uniform boundedness for the considered model. Then the linear stability analysis shows that the cross-diffusion is the key mechanism of spatiotemporal pattern formation. Amplitude equations are derived near Turing bifurcation point under nonlinear cross-diffusion to interpret pattern selection among spot pattern, stripe pattern and the mixture of spot and stripe patterns, which reflects the species's spatially inhomogeneous distribution, and it is also found that the fear factor has great influence on spatially inhomogeneous distribution of the two species under certain cross-diffusivity, that is, high level of fear can induce striped inhomogeneous distribution, low level of fear can induce spotted inhomogeneous distribution, and the intermediate level of fear can induce the mixture of spotted and striped inhomogeneous distribution. Finally, numerical simulations illustrate the effectiveness of all theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated a spatial predator–prey model with hunting cooperation in predators. Using linear stability analysis, we obtain the condition for diffusive instability and identify the corresponding domain in the space of controlling parameters. Using extensive numerical simulations, we obtain complex patterns, namely, spotted pattern, stripe pattern and mixed pattern in the Turing domain, by varying the hunting cooperation parameter in predators and carrying capacity of preys. The results focus on the effect of hunting cooperation in pattern dynamics of a diffusive predator–prey model and help us in better understanding of the dynamics of the predator–prey interaction in real environments. [ABSTRACT FROM AUTHOR]

Influenza virus mutates frequently. This poses immense challenges to prevent the spread of influenza. This paper aims to investigate an influenza epidemic model in which influenza virus can mutate into a mutant influenza virus. We find a threshold condition that determines the stability of the disease-free equilibrium. Two equilibria may also exist: mutant-dominant equilibrium and endemic equilibrium. We show that the mutant-dominant equilibrium is globally asymptotically stable under some biological feasible conditions. Furthermore, the influenza is endemic in the sense of permanence if and only if the endemic equilibrium exists. Numerical simulations are also performed to illustrate theoretical results and demonstrate the effects of disease-induced death on the dynamics of the model. [ABSTRACT FROM AUTHOR]

This paper proposes a mathematical model describing the dynamics of both Antarctic krill and Blue whale population where Antarctic krill species (prey) has group defense when they aggregate in herds in order to provide a self-defense from Blue whale species (predator). Firstly, a sufficient condition for the global asymptotical stability of the positive equilibrium is given using Poincaré–Bendixson theorem excluding periodic solution. Furthermore, we discuss the existence of Hopf-bifurcation and give criteria for stability switches through the study of a first-order exponential polynomial characteristic equation. Finally, some numerical simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

There are two families of lines describing the cell wall pattern in root and shoot apices; periclines and anticlines. The lines of these two families are mutually orthogonal and steady during apex growth. They approximate orientation of cell walls in the apices. These lines are preserved in the growing organ. The direction of periclines and anticlines is regulated at the organ level. This paper focuses on the question: how is the pattern of periclines and anticlines maintained? There are a number of rules, which deal with the problem of the orientation of a new cell wall. We test three of them: Errera rule (the smallest possible area of a new cell wall that divides the mother cell into equal portions is chosen), Sachs rule (the new wall is perpendicular to the nearest wall from the geometric center where it is inserted) and Hejnowicz postulate (the new cell wall is perpendicular to one of the principal directions of growth rate). We tested these rules in the computer simulation of the organ growth and cell divisions. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic delayed chemostat model with nutrient storage is proposed and investigated. First, we state that there is a unique global positive solution for this stochastic system. Second, using the classical approach of Lyapunov function analysis, this stochastic delayed chemostat model is discussed in detail. We establish some sufficient conditions for the extinction of the microorganism, furthermore, we prove that the microorganism will become persistent in the mean in the chemostat under some conditions. Finally, the obtained results are illustrated by computer simulations, and simulation results reveal the effects of time delay on the persistence and extinction of the microorganism. [ABSTRACT FROM AUTHOR]

Considering the delayed response to pesticide applications and the long-term residual effects of pesticides after the deployment of a pest management strategy, this paper develops a pollutant-discharge model to simulate pesticide spraying and analyze the effect of releasing natural enemies of the pest. The following two different control strategies are discussed: (1) the frequency of spraying pesticides is higher than that of releasing natural enemies, and (2) the frequency of releasing natural enemies is higher than that of spraying pesticides. For different control strategies, the sufficient conditions of locally asymptotic stability and globally asymptotic stability of the pest-eradication periodic solution are obtained. Using numerical simulations, we analyze the sensitivity of the threshold condition with respect to the parameters, identify the major factors affecting pest control and provide guidance for decision-making in pest management. Finally, we compare the control strategies and analyze which strategy is optimal as the most significant control parameters are varying. [ABSTRACT FROM AUTHOR]

This article introduces a novel model that studies the major factors jeopardizing tuberculosis (TB) control programme in China. A previously developed two-strain TB model is augmented with a class of individuals not registered under the TB control programme. The paper investigates the basic reproduction number and proves the global stability of the disease-free equilibrium. The presence of three endemic equilibria is established in the model. With the help of numerical simulations, a comparative study has been performed to test the validity of the model presented here to the real data available from the Ministry of Health of the People's Republic of China. Sensitivity and elasticity analysis give the key parameters that would govern successful TB control in China. [ABSTRACT FROM AUTHOR]

To increase a prey population that is attacked by a predator it is more convenient and economical to choose the living organisms to control the predator. In this paper, the dynamical behaviors of a prey-predator model with microparasitic infection in the predator have been discussed. In this epidemiological model the microparasite is horizontally transmitted and attacks the predator population only. The infected population does not recover or become immune. The dynamical characteristics of the system are studied through mathematical analyses. The role of discrete time-delay has been discussed to show that time-delay can induce instability and oscillation. Numerical simulations are carried out. Biological implications have been discussed. [ABSTRACT FROM AUTHOR]

A Susceptible-Infective (S-I) model is considered in this paper with time delay. The death rate is assumed to be density dependent for this model. Conditions are derived under which there can be no change in stability. Using the discrete time delay as a bifurcation parameter, we show that the model undergoes a Hopf bifurcation. The permanence conditions of the system have also been derived. Results are verified by computer simulation. [ABSTRACT FROM AUTHOR]

In this paper, a novel method to analyze the similarity/dissimilarity of protein sequences based on Principal Component Analysis-Fast Fourier Transformation (PCA-FFT) is proposed, in which, the PCA is utilized to transform protein sequences into time series and the FFT is utilized to analyze the time series while considering them as signals. To test the effectiveness of our newly proposed method, it is applied to analyze the similarity/dissimilarity of 16 different ND5 protein sequences and 29 different spike protein sequences, respectively. Furthermore, the correlation analysis is presented for comparing with others methods, and the simulation results show that it has better performances in the aspects of computation complexity and recognition degree than some existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a mathematical model of pancreatic cancer, which extends the existing pancreatic cancer models with regulatory T cells (Tregs) and Treg inhibitory therapy. The model consists of tumor-immune interaction and immune suppression from Tregs. In the absence of treatments, we first characterize the system dynamics by locating equilibrium points and determining stability properties. Next, cytokine induced killer (CIK) immunotherapy is incorporated. Numerical simulations of prognostic results illustrate that the median overall survival associated with treatment can be prolonged approximately from 7 to 13 months, which is consistent with the clinical data. Furthermore, we consider cyclophosphamide (CTX) therapy as well as the combined therapy with CIK and CTX. Intensive simulation results suggest that both CTX therapy and the combined CIK/CTX therapy can reduce the number of Tregs and increase the overall survival (OS), but Tregs and tumor cells will gradually rise to equilibrium state as long as therapies are ceased. [ABSTRACT FROM AUTHOR]

This paper studies some human immunodeficiency virus (HIV) models with switching parameters and pulse control. The classical virus dynamics model is first modified by incorporating switching parameters which are assumed to be time-varying. Some threshold conditions are derived to guarantee the virus elimination by utilizing a Razumikhin-type approach. The results show that the proper switching conditions chosen can increase the counts of CD4+ T-cells while reducing viral load. Pulse control strategies are then applied to the above model. More precisely, the treatment strategy and the vaccination strategy are applied to infected cells and uninfected cells, respectively. Each control strategy is analyzed to gauge its success in achieving viral suppression. Numerical simulations are performed to complement the analytical results and motivate future directions. [ABSTRACT FROM AUTHOR]

In this paper, we develop a two-strain SIS model on heterogeneous networks with demographics for disease transmission. We calculate the basic reproduction number of infection for the model. We prove that if , the disease-free equilibrium is globally asymptotically stable. If , the conditions of the existence and global asymptotical stability of two boundary equilibria and the existence of endemic equilibria are established, respectively. Numerical simulations illustrate that the degree distribution of population varies with time before it reaches the stationary state. What is more, the basic reproduction number does not depend on the degree distribution like in the static network but depend on the demographic factors. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a predator-prey model with a prey refuge and additional food for predators. We study the impact of a prey refuge on the stability dynamics, when a constant proportion or a constant number of prey moves to the refuge area. The system dynamics are studied using both analytical and numerical techniques. We observe that the prey refuge can replace the predator-prey oscillations by a stable equilibrium if the refuge size crosses a threshold value. It is also observed that, if the refuge size is very high, then the extinction of the predator population is certain. Further, we observe that enhancement of additional food for predators prevents the extinction of the predator and also replaces the stable limit cycle with a stable equilibrium. Our results suggest that additional food for the predators enhances the stability and persistence of the system. Extensive numerical experiments are performed to illustrate our analytical findings. [ABSTRACT FROM AUTHOR]

The most deadly Ebola outbreak in the history, which started in December , is currently under control. The high case fatality rate of the Ebola outbreak inspired local and international control strategies. In this paper, the dynamics of Ebola virus disease is modeled in the presence of three control strategies. The model describes the evolution of the disease in the population when educational campaigns, active case-finding and pharmaceutical interventions are implemented as control strategies against the disease. We prove the existence of an optimal control set and analyze the necessary and sufficient conditions, optimality and transversality conditions. We conclude through numerical simulations that containing an Ebola outbreak needs early and long-term implementation of joint control strategies. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the numerical simulation of a nonlinear stochastic partial differential equation (SPDE) arising as a model of phytoplankton aggregation. This SPDE consists of a diffusion equation with a chemotaxis term and a branching noise. We develop and implement a numerical scheme to solve this SPDE and present its numerical solutions for parameter values corresponding to real conditions in nature. Further, a comparison is made with two deterministic versions of the SPDE, that are advection-diffusion equations with linear and nonlinear reaction terms, to emphasize the efficiency of the stochastic equation in modeling the aggregation behavior in phytoplankton. [ABSTRACT FROM AUTHOR]

In this paper, we aim to propose a new chemostat model with continuous microbial culture and harvest, and to investigate the dynamics of the model. Different to the conventional ones, our model includes a constant periodic flocculant transmission. For the proposed system, by using theory of impulsive differential equations, we show that the microbe-extinction periodic solution is globally asymptotically stable when a threshold value is less than 1, and system is permanent when a certain threshold value is greater than 1. Then, according to the threshold associated with microbial extinction or existence, the control strategy for microbial continuous cultivation and harvest is discussed. Under such control strategy, continuous microbial culture and harvest can be achieved by adjusting input time, input amount or concentration of the flocculant. Finally, an example with numerical simulations is given to illustrate our theoretical conclusions. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model describing the reproduction dynamics of the Toxoplasma gondii parasite in the definitive host Felis catus (cat). The dynamics is described by a system of partial differential equations defined in a one-dimensional region, with boundary and initial conditions. The model considers both asexual and sexual reproduction processes of the T. gondii parasite starting from the consumption of T. gondii oocysts from the environment, by the definitive host, and describing the reproduction dynamics until the cat expels infectious oocysts to the environment through its feces. The numerical solution of the system is obtained, and some simulations are made, leaving constant of transition and loss rates, since its variation does not produce significant changes in the reproduction, propagation and creation of new populations; and varying the initial consumption of oocysts from the environment by the cat. It is concluded that, either low or high, the involved populations are always reproduced; they spread by all over epithelial cells and subsequently are expelled to the environment through the cat feces. It is corroborated that the cats are potential multipliers of the oocysts and therefore, the main disseminators of the infection. [ABSTRACT FROM AUTHOR]

In this paper we present a mathematical model describing the interaction of two species, a plant population and an insect population, the latter being divided in two subgroups: novice and expert pollinators. We analyze the system and show the existence of a single nontrivial equilibrium, which is stable and represents a state of mutual benefit for all species involved. We show some numerical simulations of the global stability. [ABSTRACT FROM AUTHOR]

Sudden cardiac death is mainly caused by arrhythmogenesis. For a functional abnormal heart, such as an ischemic heart, the probability of arrhythmia occurring is greatly increased. During myocardial ischemia, re-entry is prone to degenerate into ventricular fibrillation (VF). Therefore it has important meaning to investigate the intricate mechanisms underlying VF under an ischemic condition in order to better facilitate therapeutic interventions. In this paper, to analyze the functional influence of acute global ischemia on cardiac electrical activity and subsequently on re-entrant arrhythmogenesis, we take into account three main pathophysiological consequences of ischemia: hyperkalaemia, acidosis, and anoxia, and develop a 3D human ventricular ischemic model that combines a detailed biophysical description of the excitation kinetics of human ventricular cells with an integrated geometry of human ventricular tissue which incorporates fiber direction anisotropy and the stimulation activation sequence. The results show that under acute global ischemia, the tissue excitability and the slope of ventricular cellular action potential duration restitution (APDR) are greatly decreased. As a result, the complexity of VF activation patterns is reduced. For the three components of ischemia, hyperkalaemia is the dominant contributor to the stability of re-entry under acute global ischemia. Increasing [K+]o acts to prolong the cell refractory period, reduce the tissue excitability and slow the conduction velocity. Our results also show that VF can be eliminated by decreasing cellular excitability, primarily by elevating the concentration value of extracellular K+. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the effect of sex hormone binding globulin (SHBG) on the mathematical model of the hypothalamic-pituitary-gonadal (HPG) endocrine cycle which regulates the production of the male hormone testosterone. Large amounts of total circulating testosterone are bound to SHBG making them. Standard analytical techniques are used to analyze the modified mathematical model which includes a delay to account for the time required for luteinizing hormone emitted by the pituitary gland to reach the testis, to determine the steady state, its stability and the critical delay needed for the bifurcation. Numerical simulation of the solutions of the model is performed to illustrate the possible behaviors. [ABSTRACT FROM AUTHOR]

In this paper, the complex dynamics of a spatial aquatic system in the presence of self- and cross-diffusion are investigated. Criteria for local stability, instability and global stability are obtained. The effect of critical wavelength which can drive a system to instability is investigated. We noticed that cross-diffusion coefficient can be quite significant, even for small values of off-diagonal terms in the diffusion matrix. With the help of numerical simulation, we observed the Turing patterns (spots, strips, spot-strips mixture), regular spiral patterns and irregular patchy structures. The beauty and complexity of the Turing patterns are attributed to a large variety of symmetry properties realized by different values of predator's immunity, rate of fish predation and half saturation constant of predator population. [ABSTRACT FROM AUTHOR]

In this paper, we have developed a five-compartmental epidemic model with Chlamydia infection. We have divided the total population into five classes, namely susceptible, exposed, infective in asymptomatic phase, infective in symptomatic phase and recovered class. The basic reproduction number (R0) is calculated using the next-generation matrix method. The stability analysis of the model shows that the system is locally asymptotically stable at the disease-free equilibrium (DFE) E0 when R0 < 1. When R0 > 1, an endemic equilibrium E1 exists and the system becomes locally asymptotically stable at E1 under some conditions. We have also discussed the Chlamydia epidemic model with two treatment controls. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of treatment. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB, which show the reliability of our model from the practical point of view. Epidemiological implications of our analytical findings are addressed critically. [ABSTRACT FROM AUTHOR]

Considering that the ecological system is often deeply perturbed by human exploiting activities, this paper deals with a prey-predator model with prey refuge in which both species are independently harvested. First, some sufficient conditions for global stability of equilibria are obtained, and the existence and uniqueness of limit cycles are established. Our results indicate that over-exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population, which is in line with reality. Furthermore, the existence of bionomic equilibrium is discussed. Finally, the influences of prey refuge and harvesting efforts on equilibrium density values are considered and some numerical simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

A two-strain epidemic model with differential susceptibility and mutation is formulated and analyzed in this paper. The susceptible population is divided into two subgroups according to the vaccine that provides complete protection against one of the strains (strain two) but only partial against the other (strain one). The explicit formulae for the basic reproduction number and invasion reproduction number corresponding to each strain with and without mutation are derived, respectively. It is shown that there exist exclusive equilibria and coexistence equilibria, even if the reproduction number is below one. The stability of the disease-free equilibrium, strain dominance with or without mutation are investigated. The persistence of the disease is also briefly discussed. Numerical simulations are presented to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a vector-borne disease transmission model with a nonlinear incidence and vaccination. The explicit expression of the basic reproduction number R0(ϕ) which is related to the vaccination rate ϕ is obtained. It has been shown that the global dynamical behavior of the model is completely determined by R0(ϕ). If R0(ϕ) < 1, the disease-free equilibrium (DFE) is globally asymptotically stable, and the disease will be eradicated. If R0(ϕ) > 1, the DFE is unstable, and there exists a unique endemic equilibrium (EE). This equilibrium is globally asymptotically stable which in turn causes the disease to persist in vectors and humans. Finally, a series of numerical simulations, such as sensitive analysis on R0(ϕ), are performed in order to support the theoretical results. [ABSTRACT FROM AUTHOR]

Substance abuse remains a global menace in spite of recurrent warnings, seizures, social and pharmacological effects associated with addiction to drugs. In this paper, we use a mathematical model which is a combination of the classical SIS and SIR models to investigate the dynamics of substance abuse. Initiation into drug use is based on con-tact of those at risk (the susceptible population) with drug users at different levels of drug use. We evaluate the threshold number and use it to analyze the model. We show that when this threshold number is less than unity, the drug-free steady state is glob-ally asymptotically stable and when this threshold number is greater than unity the drug-persistent steady state is also globally stable. The impact of amelioration, reha-bilitation and re-initiation on drug epidemics is investigated. Amelioration in presence of quitting for light users is observed to reduce the prevalence of substance abuse and this is supported by numerical simulations. The results show that both prevention and treatment/rehabilitation are necessary strategies for reduction of drug epidemics. Our recommendation is that preventive strategies should be directed toward reducing the contact rate and treatment should be combined with psychotherapy to accelerate quit-ting and reduce re-initiation. [ABSTRACT FROM AUTHOR]

In this paper, two mathematical models are proposed and analyzed. The first one deals with the interaction of uninfected cells, infected cells, viruses and immune response within humans. The second one deals with the effects of environmental toxicant on the first model. In each case, sufficient conditions for local stability and global stability of the equilibria are obtained, computer simulations are performed and the result is biologically interpreted. It has been seen that the environmental toxicant has detrimental effects on healthy cells, infected cells as well as on the immune response of the body. [ABSTRACT FROM AUTHOR]

In this paper we present a susceptible-infectious-susceptible (SIS) model that describes the transmission dynamics of cutaneous Leishmaniasis. The model treats a vector population and several populations of different mammals. Members of the human population serve as the incidental hosts, and members of the various animals populations serve as reservoir hosts. We establish the basic reproduction number and the equilibrium conditions of the system. We use a generalization of the Lyapunov function approach to show that when the basic reproduction number is less than or equal to one, the diseases-free equilibrium is a global attractor, and that when it is greater than one the endemic equilibrium is a global attractor. We present numerical simulations that demonstrate the dynamics of the model for a system containing a human population and a single animal population. [ABSTRACT FROM AUTHOR]

Eubank et al. propose to study the spread of infectious disease in large urban environments using dynamic bipartite graph modeling the contact pattern, and computer simulations to estimate the evolution of epidemics. Eubank's approach requires a detailed knowledge of individuals, daily routine. In our work we would generalize the model by introducing a stochastic relocation of people and vectors among locations, thanks to distribution functions. Computer simulations are used to produce the infection and death processes. Finally, the paper presents two case studies. The first case study emphasizes the effect of using probabilistic relocation in a particular social network, while the second discusses how vector-borne diseases could be taken into account. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a nonautonomous stage-structured epidemic model having two stages of the period of infection according to the progressing process of some infectious diseases (e.g. Chagas' disease, hepatitis C, etc.) with varying total population size and distributed time delay to become infectious. The infected persons in the different stages have different ability of transmitting disease. We have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical technique. We have obtained the explicit formula of the eventual lower bounds of infected persons. We have introduced some new threshold values R0 and R* and further obtained that the disease will be permanent when R0 > 1 and the disease will be going to extinct when R* < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness. [ABSTRACT FROM AUTHOR]