Search

The paper discusses the nutrient-plankton system with effect of time delay in nutrient recycling and toxin-determined function response (TDFR). The designed model system explores the delay-induced system dynamics. We present the local stability analysis of interior equilibrium points in absence as well as in presence of time delay. Further, the direction of Hopf bifurcation is obtained. We perform the numerical computation and observe that time delay in nutrient recycling can generate the periodic solution in a stable nutrient-plankton system. Some other essential parameters, such as input concentration of nutrients and natural removal rate of nutrients, also regulate the dynamical system. The system shows Hopf and double-Hopf bifurcation in the presence of time delay. Our study shows that the delay in the nutrient recycling causes instability transition phenomenon. The delay-induced nutrient recycling and different input concentrations of nutrients can regulate the estuarine system. Finally, the stability switching is observed for delayed system. [ABSTRACT FROM AUTHOR]

Neurons can exhibit various rhythmic activities such as bursting, spiking, and quiescent states when exposed to external input current stimulus. In this paper, a model of medicinal leech's heart (LH) interneuron is considered to describe the dynamics of neurons with a varied range of electrical activities. The crucial insights into the model's dynamics are explored in three different parameter regimes: phasic spiking, regular spiking, and bursting, based upon the codimension-one bifurcation of the model by considering V K 2 s h i f t as a bifurcation parameter. The spatiotemporal dynamics of the model are explored by allowing 1D and 2D diffusion in the membrane voltage. The 1D diffusive system produces irregular bursting dynamics for the intermediate value of diffusion coefficients, whereas, at higher values, it shows synchronized oscillations. In the presence of 2D diffusion, the emergence of different types of spiral patterns is observed in the system. Furthermore, the system is extended by incorporating electromagnetic induction in the membrane voltage to explore the effect of induction on the various dynamics of neural model. By varying its intensities, the membrane voltage in the extended model produces a variety of discharge modes, such as periodic spiking, fast-spiking, resting, and spike-adding phenomena. In addition, the emergence of anti-spiral patterns in the extended model near subcritical Hopf bifurcation is analytically verified using the complex Ginzburg-Landau equation (CGLE). These findings demonstrate that the firing patterns vary based on the control parameters, and these variations contribute to our understanding of how the brain system transmits and processes the signals. • A slow-fast neuron model of Leech's heart interneuron is considered. • The model is improved by adding EMI to study the impact of magnetic flux. • Bifurcation scenarios and different firing activities of both models are performed. • These systems with diffusion display irregular firing and multi-arm spiral patterns. • CGLE analysis in the system with EMI confirms anti-spiral patterns occurrence. [ABSTRACT FROM AUTHOR]

Few existing studies establish the fact that although human pathogen exists in the environmental reservoir, infectious disease outbreak is rare. In this article, we investigate the dynamics of cholera disease where the transmission occurs via contact with a contaminated reservoir. A deterministic iSIR compartmental epidemic model is formulated and explored the realistic situation, in which the quantity of ingested pathogens must exceed a critical threshold, the minimal infectious dose (MID), in order to infect healthy population. Bacteria growth rate is considered to follow the Allee effect. This model system shows multi-stability and undergoes transcritical and saddle-node bifurcations with respect to various parameters. Thus, external environmental noise can give rise to observable dynamics for the stochastic counterpart. One can see a noise-induced frequent transitions between two separate interior attractors, in particular for the cases where the deterministic model displays bistability. The global sensitivity using PRCC method is performed. Also, the optimal control for the developed deterministic cholera epidemic model is carried out with numerical illustrations. Our model primarily designed to explain and predict the indirectly transmitted cholera epidemic model incorporating the idea of MID. This study gives a different outlook for the transmission of disease from the human-centered perspective to socioeconomic context. [ABSTRACT FROM AUTHOR]

In the current study, we have formulated an S I epidemic model incorporating the influence of Allee effect on the dynamics of the model system in space and time. During the spread of the disease, inhibition among the susceptible and infected individuals is seen, which is measured using the Crowley–Martin type incidence function. Extensive analysis explores the system's stability and different bifurcation scenarios, including Hopf, saddle-node, transcritical, and Bogdanov–Takens. We also examine how these bifurcations react to parameter variations within the proposed model. The temporal model has further been extended to a spatial one to investigate the impact of the Allee effect on the formation of patterns for different values of the cross-diffusion coefficient. The well-posedness of the stationary solution and the global stability of the spatial system are derived. Also, the Turing instability, Hopf, and Turing bifurcation are calculated considering the transmission rate as critical parameter. In a heterogeneous environment, the spatial distribution of the susceptible population shows a complex structure with flat tabular surface and a few almost circular holes in surface plots for both strong and weak Allee effects. To further explore the role of Allee effect on pattern development for various cross-diffusion coefficient values, the temporal model has been spatially extended. Additionally, the transmission rate is taken into account while calculating the Turing instability and Hopf and Turing bifurcations. We ran numerical simulations to validate our analytical results for both spatial and nonspatial models. Our current model system can explain the recent occurrence of respiratory distress syndrome in endangered penguin species. [ABSTRACT FROM AUTHOR]

Predator–prey interactions do not solely depend on biotic factors: rather, they depend on many other abiotic factors also. One such abiotic factor is wind speed, which can crucially change the predation efficiency of the predator population. In this article, the impact of wind speed along with seasonality on various parameters has been investigated. Here, we present two continuous-time models with specialist and generalist type predators incorporating the effect of wind and the seasonality on the model parameters. It has been observed that wind speed plays a significant role in controlling the system dynamics for both systems. It makes the systems stable for both of the seasonally unperturbed systems. However, it controls the chaotic dynamics that occur in case of no wind for the seasonally perturbed system with the predator as a specialist. On the other hand, for the seasonally perturbed system with a generalist predator, it controls period-four oscillations (which occur considering no wind speed) to simple limit-cycle oscillations. Furthermore, the wind parameter has a huge impact on the survival of predator species. The survival of predator species may be achieved by ensuring a suitable range of wind speeds in the ecosystem. Therefore, we observe that seasonality introduces chaos, but wind reduces it. These results may be very useful for adopting necessary management for the conservation of endangered species that are massively affected by wind speed in an ecosystem. [ABSTRACT FROM AUTHOR]

The dynamics of infectious disease transmission depends on social contact patterns and the precautions people take to minimize disease transmission. The social contact pattern varies depending on the community at large age distribution at work, school, and recreation. Consequently, knowing the age-specific prevalence and incidence of infectious diseases is critical for predicting future disease burden and the efficacy of interventions like vaccination. In this study, we use an SEIR age-structured multi-group epidemic model to understand how social contact affects disease control. We construct location-specific social contact matrices to observe that how social mixing affects disease spread. For mathematical analysis, we compute the basic reproduction number (R 0) and exhibit the global behavior of the system in terms of R 0 . We also estimate the transmission rate using the empirical data of COVID-19 for India from 1 September 2020, to 31 December 2020. We simulate the lifting of non-pharmaceutical interventions by allowing people to return to work in phases and investigate its impact. Our findings imply that raising awareness in symptomatic infected individuals aged 20–49 years can help in reducing the number of infected individuals. When some schools are partially open, awareness in symptomatic infected individuals in school-age groups also plays a significant role in reducing disease cases. The simulation results also suggest that limiting contact at school and other gathering places could significantly lower the number of instances. Using the least square approach, we show that the time-dependent transmission rate is more realistic than the constant spread rate for COVID-19 in India. To reduce the COVID-19 burden, we obtain that gradually loosening control measures could flatten and lower other peaks. Our findings may help health policymakers to decide on timely age-based vaccination distribution strategies and control measures. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to explore a new delayed epidemiological model assuming that the disease is transmitted among the susceptible population and possessing nonlinear incidence function along with a saturated treatment rate. Due attention is paid to the positivity and boundedness of the solutions and the bifurcation of the dynamical system as well. Basic reproduction number is being calculated, and considering the latent period as a bifurcation parameter, it has been examined that a Hopf-bifurcation occurs near the endemic equilibrium point while the parameter attains critical values. We have also discussed the stability and direction of Hopf-bifurcation near the endemic equilibrium point, the global stability analysis and the optimal control theory. We conclude that the system reveals chaotic dynamics through a specific time-delay value. Numerical simulations are being performed in order to explain the accuracy and effectiveness of the acquired theoretical results. [ABSTRACT FROM AUTHOR]

The anti-predator element because of fear from predator population in prey–predator models has an excellent significance and it is able to lessen the duplicate of prey population to a positive degree. In this paper, a delayed prey–predator model including fear effect and predator-taxis sensitivity is studied. Local stability and occurrence of Hopf bifurcation are analyzed by fixing the time delay as the bifurcating parameter. Then, a series of sufficient criteria for global stability is established by designing a suitable Lyapunov function. Furthermore, direction and stability of the Hopf bifurcation are studied. Lastly, numerical simulation outcomes are performed to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

In this study, we present a delayed predator–prey model with cannibalism including a prey, a juvenile predator and an adult predator. The adult predator hunts not only the prey but also the juvenile predator. The alternative resource is considered to reduce cannibalism in predator species. The main results are demonstrated by local stability and Hopf bifurcation. Sufficient criteria for local stability of the interior equilibrium point and the exhibition of a Hopf bifurcation are derived. Global stability is analyzed via designing a suitable Lyapunov function. Additionally, stability of the Hopf bifurcation is explored. Finally, numerical simulations are executed to validate the obtained results. [ABSTRACT FROM AUTHOR]

Simple Summary: This article provides original numerical and mathematical insights about the FHR model and non-homogeneous FitzHugh–Nagumo reaction-diffusion systems. This article focuses on the qualitative analysis of complex dynamics arising in a few mathematical models in neuroscience context. We first discuss the dynamics arising in the three-dimensional FitzHugh–Rinzel (FHR) model and then illustrate those arising in a class of non-homogeneous FitzHugh–Nagumo (Nh-FHN) reaction-diffusion systems. FHR and Nh-FHN models can be used to generate relevant complex dynamics and wave-propagation phenomena in neuroscience context. Such complex dynamics include canards, mixed-mode oscillations (MMOs), Hopf-bifurcations and their spatially extended counterpart. Our article highlights original methods to characterize these complex dynamics and how they emerge in ordinary differential equations and spatially extended models. [ABSTRACT FROM AUTHOR]

Synchronization of food chain models is an intensely investigated area in dynamical systems. Two pioneering models in three species food chain systems exhibiting chaotic dynamics are the Hastings and Powell (HP) model and the Upadhyay and Rai (UR) model. These are known to synchronize, even though the top predators in the two models behave differently. In the current manuscript, we show that although the HP and UR models synchronize for certain initial conditions, they do not synchronize for arbitrarily large initial conditions due to the blow-up dynamics present in the UR model. Thus, the synchronization of these model systems is purely a local (in initial data) phenomenon. Interestingly, we find that a similar result holds for the modified UR model as well, which has global in-time solutions for any positive initial condition. Thus, the lack of synchrony could also be attributed to the difference in the top predator's feeding preferences in the model systems. Our results have large-scale applications to population synchrony in tri-trophic food chains. [ABSTRACT FROM AUTHOR]

We employ an age-structured susceptible-infected-quarantined-recovered model to simulate the progression of COVID-19 in France, Spain, and Germany. In the absence of a vaccine or conventional treatment, non-pharmaceutical interventions become more valuable, so our model takes into account the efficacy of official social distancing and lockdown measures. Using data from February to July 2020, we make useful predictions for the upcoming months, and further simulate the effect of lifting the lockdown at a later stage. A control model is also proposed and conditions for optimality are also obtained using optimal control theory. Motivated by the recent surge in cases in France and Spain, we also examine the possibility of a second wave of the pandemic. We conclude that further measures need to be taken in these two countries, while Germany is on its way to mitigating the disease. [ABSTRACT FROM AUTHOR]

• An attempt has been made to understand the effect of electromagnetic induction on the network of neurons. • An excitable slow-fast memristive model has been studied with its various intrinsic dynamics. • We analytically establish the existence and stability of Hopf bifurcation with bifurcating periodic solutions. • We investigate the emergence of multi-arm antispiral waves in the system with proper analytical justification. • A random network architecture is used to study the dynamics of coupled network that generates MMOs and bursting patterns. The diverse firing responses in a single neuron model as well as in a neuronal network play a major role in understanding the collective neuronal dynamics. In this paper, we consider an excitable slow-fast memristive model and study its various intrinsic dynamics by allowing a periodic external stimulus. The single model exhibits various types of spiking, bursting, mixed-mode oscillations (MMOs), and mixed-mode bursting oscillations (MMBOs) depending on the amplitude and frequency of the periodic injected current. Corresponding bifurcation analysis reveals the existence of supercritical and subcritical Hopf bifurcations in the system depending on the major predominant parameters that establish the scenarios of the neuronal responses. We have verified analytically the existence and stability of Hopf bifurcations. The memristive system can produce cascade of period doubling bifurcations for particular parameter regimes. Next, we investigate the emergence of multi-arm antispiral waves in the diffusively coupled system with proper analytical justification. We have also computed the group and phase velocities to discern the spiral and antispiral waves near the Hopf instability. A transition from target wave to multi-arm antispiral wave is observed in the diffusive system. Moreover, we use a random network architecture different from the diffusive network to study the dynamics of the coupled network for certain firing activities. It is observed that the network of heterogeneous desynchronized neurons with higher electrical couplings, can generate MMOs, MMBOs, and bursting for different external stimuli. However, the uncoupled systems cannot reveal such typical dynamics for particular parameters. Further, we introduce a reduced-order model to summarize the complete dynamics of the larger random network and report the findings. [ABSTRACT FROM AUTHOR]

Smoking poses an enormous threat to public health in the globe and continues to be one of the main cause of health problems. In this paper, a delayed smoking model with reversion class is proposed. Local stability of the smoking equilibrium and Hopf bifurcation is analyzed by taking the time delay as the bifurcation parameter. In particular, global exponential stability is proved by using the linear matrix inequality method. The theoretical results obtained are validated numerically and graphically. [ABSTRACT FROM AUTHOR]

In this article, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modeled using the nearest neighbor coupling theory, in which the diffusion part measures the spatial distribution of coupling topology. We derive analytically the conditions for traveling wave profiles that allow the construction of the shape of traveling nerve impulses. The analytical and numerical results are used to explore the nature of propagating pulses. The symmetric or asymmetric nature of traveling pulses is characterized, and the wave velocity is derived as a function of system parameters. Moreover, we present our results for an extended excitable medium by considering a slow-fast biophysical model with a homogeneous, diffusive coupling that can exhibit various traveling pulses. The appearance of series of pulses is an interesting phenomenon from biophysical and dynamical perspective. Varying the perturbation and coupling parameters, we observe the propagation of activities with various amplitude modulations and transition phases of different wave profiles that affect the speed of pulses in certain parameter regimes. We observe different types of traveling pulses, such as envelope solitons and multi-bump solutions, and show how system parameters and coupling play a major role in the formation of different traveling pulses. Finally, we obtain the conditions for stable and unstable plane waves. [ABSTRACT FROM AUTHOR]

Recent field experiments have shown that predators influence the prey population not only by direct consumption but also by stimulating various defensive strategies. The cost of these defensive strategies can include energetic investment in defensive structures, reduced energy income, lower mating success, and emigration which ultimately reduces the reproduction of prey. To explore the effect of these defensive strategies (anti‐predator behaviors), a modified Leslie–Gower predator–prey model with the cost of fear has been considered. Gestation delay is also incorporated in the system for a more realistic formulation. Boundedness, equilibria and stability analysis are performed for the temporal system. By considering gestation delay as a bifurcation parameter, the existence of Hopf‐bifurcation around the interior equilibrium point is discussed together with the direction, stability, and period of bifurcating solutions arising through Hopf‐bifurcation. The spatial extension of the proposed model incorporating density‐dependent cross‐diffusion is also investigated and the conditions for diffusion‐driven instability are obtained. To illustrate the analytical findings, detailed numerical simulations are performed. Biologically realistic Turing patterns such as spots, spots and stripes mixture, and labyrinthine type patterns are identified. It is found that the fear level has a stabilizing impact on delay induced destabilization and both stabilizing and destabilizing effects on Turing instability. [ABSTRACT FROM AUTHOR]

In this paper, attempt has been made to grasp the idea about the role of fear effect of intermediate specialist predator on prey and the effect of the top predator interference in the spatial framework of a three species food chain model. By introducing a hybrid model and assuming that the interaction between prey and intermediate predator obeys the Volterra scheme, whereas Beddington-DeAngelis (BD) type functional response is taken in between the top predator and its favorite food. The stability properties of each equilibrium point of the temporal model system, blow up in finite time for both temporal and spatial systems corresponding to a large initial data are established. We pay attention to illustrate different types of patterns around the neighbourhood of a critical parameter. Choosing appropriate control parameter from the Turing space and using the existence criteria, stable patterns are obtained. The result of theoretical analysis well agrees with the result exhibited through numerical simulations around the critical parameter. Finally, numerical simulation illustrates the role of diffusion in the spatial domain by formations of different patterns. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a mathematical model of plankton dynamics in an aquatic system. We consider the fact that phytoplankton take refuge and release toxic chemicals to reduce their predation by the zooplankton who is assumed to be a generalist predator. We make the system more realistic with the inclusion of seasonal variations of the model parameters representing input of nutrients, refuge taken by phytoplankton, toxins released by phytoplankton and supply of additional foods for zooplankton. The autonomous and nonautonomous systems are analyzed mathematically, and numerical simulations explore various dynamics of both the systems. In the absence of seasonal forcing, we observe that the system destabilizes on a gradual increase in the input rate of nutrients and recycling of dead biomass of phytoplankton into nutrients concentration. In contrast, refuge taken by phytoplankton, toxins liberation by phytoplankton and intraspecific competition among the species of phytoplankton have potentials to terminate the persistent oscillations, and bring stability in the ecosystem. Supply of additional foods to zooplankton in low (high) quantity creates instability (stability) in the planktonic system. Moreover, in the presence of seasonal forcing, we observe different dynamical features including periodic solution, higher periodic solutions, bursting patterns and boundary periodic solution. Overall, our findings not only provide insights about the sustainability of biodiversity by potentially explaining the emergence of seasonally recurring planktonic blooms, but also could be employed to assist develop management strategies to preserve and restore the integrity of an aquatic habitat. [ABSTRACT FROM AUTHOR]

The recent emergence of COVID-19 has drawn attention to the various methods of disease control. Since no proper treatment is available till date and the vaccination is restricted to certain age groups, also vaccine efficacy is still under progress, the emphasis has been given to the method of isolation and quarantine. This control is induced by tracing the contacts of the infectious individuals, putting them to the quarantine class and based on their symptoms, classifying them either as the susceptible or sick individuals and moving the sick individuals to the isolated class. To track the current pandemic situation of COVID-19 in India, we consider an extended Susceptible-Exposed-Quarantine-Infected-Isolated-Recovered (SEQ1IQ2R) compartmental model along with calculating its control reproductive number Rc. The disease can be kept in control if the value of Rc remains below one. This "threshold" value of Rc is used to optimize the period of quarantine, and isolation and have been calculated in order to eradicate the disease. The sensitivity analysis of Rc with respect to the quarantine and isolation period has also been done. Partial rank correlation coefficient method is applied to identify the most significant parameters involved in Rc. Based on the observed data, 7-days moving average curves are plotted for prelockdown, lockdown and unlock 1 phases. Following the trend of the curves for the infection, a generalized exponential function is used to estimate the data, and corresponding 95% confidence intervals are simulated to estimate the parameters. The effect of control measures such as quarantine and isolation are discussed. Following various mathematical and statistical tools, we systematically explore the impact of lockdown strategy in order to control the recent outbreak of COVID-19 transmission in India. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of a stage-structured SI epidemic system with a saturated incidence rate and a saturated treatment function. Two discrete time delays are incorporated to represent the time required for immature to be mature, and the infected individuals to move into recover class, respectively. A thorough investigation of endogenous equilibrium states of the SI system has been conducted, and the characteristics of the dynamical system around these states, including local stability and Hopf bifurcation, have been studied. Using sensitivity analysis, the model is evaluated to determine which parameters play greater roles in the model results and subsequently which of them may be used to control the disease. Finally, some numerical simulations have been conducted to confirm the analytical results. [ABSTRACT FROM AUTHOR]

An e-epidemic SIRS (susceptible-infected-recovered-susceptible) model is proposed with a generalized non-monotone incidence rate characterizing the psychological effect of some devastating malware when the number of infected nodes are getting larger. Existence of unique and multiple equilibria, linear and non-linear stability with the help of basic reproduction number, and the nature of temporal system dynamics are analyzed. Bifurcation analyses (backward and forward transcritical bifurcation, Hopf bifurcation) are performed that are exhibited by the temporal system. It has been shown that saturation recovery of infected nodes along with the malware transmission rate lead to vital dynamics such as monostable and bistable, when basic reproduction number ( R 0 ) is less than unity. Further, state feedback controller is introduced along with the time delay for extending the region of stability and delaying the occurrence of Hopf bifurcation in the network. All the analytical results are validated through numerical simulation experiments. Numerically, it reflects that a larger value of inhibition factor, a and smaller value of γ can accelerate the malware removal and reduces the infection level in the network. Our study helps to understand how the psychological effect impacts on the network malware propagation process. The analysis and simulation results are useful for the policy-making insights of the anti-malware practices in the information sharing networks. [ABSTRACT FROM AUTHOR]

Pandemic is an unprecedented public health situation, especially for human beings with comorbidity. Vaccination and non-pharmaceutical interventions only remain extensive measures carrying a significant socioeconomic impact to defeating pandemic. Here, we formulate a mathematical model with comorbidity to study the transmission dynamics as well as an optimal control-based framework to diminish COVID-19. This encompasses modeling the dynamics of invaded population, parameter estimation of the model, study of qualitative dynamics, and optimal control problem for non-pharmaceutical interventions (NPIs) and vaccination events such that the cost of the combined measure is minimized. The investigation reveals that disease persists with the increase in exposed individuals having comorbidity in society. The extensive computational efforts show that mean fluctuations in the force of infection increase with corresponding entropy. This is a piece of evidence that the outbreak has reached a significant portion of the population. However, optimal control strategies with combined measures provide an assurance of effectively protecting our population from COVID-19 by minimizing social and economic costs. [ABSTRACT FROM AUTHOR]

This article reports a method for the estimation of parameters of a 3D Hindmarsh Rose neural model under a noisy measurement. Estimation procedure is based on reparametrization of the 3D model in a linear form. Method of least square has been used to estimate the biophysical parameters of the model. It is known that the presence of unavoidable noise effects the estimation procedure. To reduce the influence of noise to a certain extent, a denoising algorithm based on local projection is considered. Estimation procedure has been derived both in noisy and denoised condition to present the effectiveness of the algorithm. The denoising technique has been applied to reduce the influence of noisy stimuli in an experimentally collected EEG data set and the results are presented in terms of reduction in variance level. The effectiveness of the method is presented using analytical/mathematical and simulation results. [ABSTRACT FROM AUTHOR]

Fear of top predators may be as or more important than direct killing in causing trophic cascades. The mere presence of top predators gives rise to a "landscape of fear", buffering lower trophic levels from overconsumption by herbivores. In the present work, we have proposed a three-species food chain model of wolf spiders (top predator), insect pests (herbivores), and plant community interactions incorporating the cost of fear of wolf spiders in the predation rate of insect pests. It is assumed that some of the insect pests migrate due to the fear of wolf spiders. Positivity, boundedness, and parameter regimes for an ecologically realistic parameter set is identified. We have derived the local and global stability conditions for the proposed system. The existence of Hopf-bifurcation, direction and stability conditions of the bifurcating periodic solutions have been discussed. It is observed that the fear of wolf spiders has a stabilizing impact on system dynamics. It contributes positively to the role of wolf spiders as a biocontrol agent. One and two-parameter bifurcation diagrams have been plotted. It is observed that fear level decreases with an increase in the migration rate and for relatively large values of conversion rate, insect pests become less sensitive toward the perceived predation risk. [ABSTRACT FROM AUTHOR]

The article focuses on the issue of a spatiotemporal excitable biophysical model that describes the propagation of electrical potential called spikes to model the diffusion-induced dynamics based on an analytical development of amplitude equations. Considering the Izhikevich neuron model consisting of coupled systems of ODEs, we demonstrate various results of spatiotemporal architecture (PDEs) using a suitable parameter regime. We analytically perform the saddle-node bifurcation and Hopf bifurcation analysis with bifurcating periodic solutions that show the transition phases in the system dynamics. We study different firing patterns both analytically and numerically by the formation of Riccati differential equation. To examine the characteristics of diffusive instabilities, we use Turing amplitude equations by multiscaling method. The instabilities and Turing bifurcation are established using theoretical analysis and numerical simulations. The spatial dynamics has potential effects on the deterministic system as a result of the diffusive matrices with various couplings, and the coupled oscillators with this nearest-neighbor coupling show synchronization measured by the synchronization factor analysis. Our results qualitatively reproduce different phenomena of the extended excitable system based with an efficient analytical scheme. [ABSTRACT FROM AUTHOR]

In this article, we construct an excitable memristive diffusive neuron model by considering a biophysical slow–fast bursting oscillator and study the effects of electromagnetic induction on the dynamics of the single model as well as the coupled systems. We explore various firing regimes such as tonic spiking, bursting, and mixed-mode oscillations depending on the bifurcation structure with different injected current stimuli, then perform a comparative analysis on the synchronization of the coupled oscillators by setting the model into two different network architectures. First, a diffusively coupled network is considered, and later a global network is constructed. The results suggest that the diffusively connected neurons show complete synchronization at higher couplings for bursting and tonic spiking regimes. Furthermore, we show that the extended spatial system can generate spiral-like patterns in the vicinity of a Hopf bifurcation point and observe the impact of Gaussian white noise to study its effects on pattern formation. These types of patterns are robust in the excitable model. Our results might contribute significantly to the dynamical studies of irregular neural computation. [ABSTRACT FROM AUTHOR]

In this paper, we have proposed a model system of two preys that mutually contribute to each other with restricted growth rates upon arrival of a generalist predator (who can sexually reproduce) whose predation is followed by Holling type II functional response where three species are self-diffusing for their best of the survival. In spatial case, we investigate the conditions of the blow-up phenomena of sexually reproductive predator of generalist category at finite time. The stability of the system is studied, and we discuss about the conditions of Turing instability. Near bifurcation threshold, major slow down in the dynamical system has been noticed. Variation in the dynamical behaviour of the model system makes structural changes which suggests emergence of patterns. Lastly via numerical simulation, we illustrate different significant patterns such as spots, spots-stripes and stripes which are generated by variation of diffusion parameters and investigate the transition from chaotic to stability properties of the system. Finally, we explain our obtained results where prey exhibits mutual relation among themselves and investigate the populations of the alien/invasive species being fulminated in the ecosystem. [ABSTRACT FROM AUTHOR]

The analysis of dynamical complexity in nonlinear phenomena is an effective tool to quantify the level of their structural disorder. In particular, a mathematical model of tumor-immune interactions can provide insight into cancer biology. Here, we present and explore the aspects of dynamical complexity, exhibited by a time-delayed tumor-immune model that describes the proliferation and survival of tumor cells under immune surveillance, governed by activated immune-effector cells, host cells, and concentrated interleukin-2. We show that by employing bifurcation analyses in different parametric regimes and the 0–1 test for chaoticity, the onset of chaos in the system can be predicted and also manifested by the emergence of multi-periodicity. This is further verified by studying one- and two-parameter bifurcation diagrams for different dynamical regimes of the system. Furthermore, we quantify the asymptotic behavior of the system by means of weighted recurrence entropy. This helps us to identify a resemblance between its dynamics and emergence of complexity. We find that the complexity in the model might indicate the phenomena of long-term cancer relapse, which provides evidence that incorporating time-delay in the effect of interleukin in the tumor model enhances remarkably the dynamical complexity of the tumor-immune interplay. [ABSTRACT FROM AUTHOR]

The Zika virus (ZIKV) epidemic is depicted to have high spatial diversity and slow growth, attributable to the dynamics of the mosquito vector and mobility of the human populations. In an effort to understand the transmission dynamics of Zika virus, we formulate a new compartmental epidemic model with a system of seven differential equations and 11 parameters incorporating the decaying transmission rate and study the impact of protection measure on basic public health. We do not fit the model to the observed pattern of spread, rather we use parameter values estimated in the past and examine the extent to which the designed model prediction agrees with the pattern of spread seen in Brazil, via reaction–diffusion modeling. Our work includes estimation of key epidemiological parameters such as basic reproduction number ( R 0) , and gives a rough estimate of how many individuals can be typically infected during an outbreak if it occurs in India. We used partial rank correlation coefficient method for global sensitivity analysis to identify the most influential model parameters. Using optimal control theory and Pontryagin's maximum principle, a control model has been proposed and conditions for the optimal control are determined for the deterministic model of Zika virus. The control functions for the strategies (i) vector-to-human contact reduction and (ii) vector elimination are introduced into the system. Numerical simulations are also performed. This work aimed at understanding the potential extent and timing of the ZIKV epidemic can be used as a template for the analysis of future mosquito-borne epidemics. [ABSTRACT FROM AUTHOR]

Robust testing and tracing are key to fighting the menace of coronavirus disease 2019 (COVID-19). This outbreak has progressed with tremendous impact on human life, society and economy. In this paper, we propose an age-structured SIQR model to track the progression of the pandemic in India, Italy and USA, taking into account the different age structures of these countries. We have made predictions about the disease dynamics, identified the most infected age groups and analysed the effectiveness of social distancing measures taken in the early stages of infection. The basic reproductive ratio R 0 has been numerically calculated for each country. We propose a strategy of age-targeted testing, with increased testing in the most proportionally infected age groups. We observe a marked flattening of the infection curve upon simulating increased testing in the 15–40 year age groups in India. Thus, we conclude that social distancing and widespread testing are effective methods of control, with emphasis on testing and identifying the hot spots of highly infected populations. It has also been suggested that a complete lockdown, followed by lockdowns in selected regions, is more effective than the reverse. [ABSTRACT FROM AUTHOR]

The objective of this paper is to propose a delayed susceptible-infectious-recovered (SIR) model for the transmission of porcine reproductive respiratory syndrome virus (PRRSV) among a swine population, including the latent period delay of the virus and the time delay due to the period the infectious swines need to recover. By taking different combinations of the two delays as the bifurcation parameter, local stability of the disease-present equilibrium and the existence of Hopf bifurcation are analyzed. Sufficient conditions for global stability of the disease-present equilibrium are derived by constructing a suitable Lyapunov function. Directly afterwards, properties of the Hopf bifurcation such as direction and stability are studied with the aid of the normal form theory and center manifold theorem. Finally, numerical simulations are presented to justify the validity of the derived theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a delayed tobacco smoking model containing users in the form of snuffing. Its dynamics is studied in terms of local stability and Hopf bifurcation by regarding the time delay as a bifurcation parameter and analyzing the associated characteristic transcendental equation. Specially, specific formulas determining the stability and direction of the Hopf bifurcation are derived with the aid of the normal form theory and the center manifold theorem. Using LMI techniques, global exponential stability results for smoking present equilibrium have been presented. Computer simulations are implemented to explain the obtained analytical results. [ABSTRACT FROM AUTHOR]

Many prey organisms have developed defense mechanisms against predation. If the predator can encounter in a limited spatial domain, the feeding rates reflect interference between predators and the corresponding functional response depends on both predator and prey densities. In this manuscript, an attempt has been made to understand the role of top predator interference and gestation delays on the dynamics of a three-species food chain model involving intermediate and top predators population. Interaction between the prey and an intermediate predator follows the Monod–Haldane functional response, while that between the top predator and its prey depends on Beddington–DeAngelis-type functional response. Analytically, we study the essential mathematical features such as boundedness, stability and direction of bifurcating periodic solution around the coexisting equilibrium for the model system. Numerically, we study the Hopf and transcritical bifurcations scenarios with respect to inhibitory effect of phytoplankton against zooplankton and death rate of fish population for the non-delayed system. Further, we study the stability behavior of the delayed model system. Model system exhibits irregular behavior when the interference is high or gestation period is larger than its critical value. Further, the system shows extinction of predators with the increase in inhibitory effect. Stability domain plots with respect to different important system parameters for non-delayed system and delay parameters for delayed system give a significant impact to study the stability of the different equilibrium points and bifurcation scenarios of both non-delayed and delayed systems. Our results point out the complexity of three-way interactions between phytoplankton, zooplankton and fish population in marine environment and highlight the role of predator interference and gestation delays in exhibiting the chaotic dynamics and extinction of predator population. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to understand the role of predator's interference and additional food on the dynamics of a diffusive population model. We have studied a predator–prey interaction system with mutually interfering predator by considering additional food and Crowley–Martin functional response (CMFR) for both the reaction–diffusion model and associated spatially homogeneous system. The local stability analysis ensures that as the quantity of alternative food decreases, predator-free equilibrium stabilizes. Moreover, we have also obtained a condition providing a threshold value of additional food for the global asymptotic stability of coexisting steady state. The nonspatial model system changes stability via transcritical bifurcation and switches its stability through Hopf-bifurcation with respect to certain ranges of parameter determining the quantity of additional food. Conditions obtained for local asymptotic stability of interior equilibrium solution of temporal system determines the local asymptotic stability of associated diffusive model. The global stability of positive equilibrium solution of diffusive model system has been established by constructing a suitable Lyapunov function and using Green's first identity. Using Harnack inequality and maximum modulus principle, we have established the nonexistence of nonconstant positive equilibrium solution of the diffusive model system. A chain of patterns on increasing the strength of additional food as spots → stripes → spots has been obtained. Various kind of spatial-patterns have also been demonstrated via numerical simulations and the roles of predator interference and additional food are established. [ABSTRACT FROM AUTHOR]

This paper considers a plankton–fish interaction model by comparing the dynamics between non-spatial and spatial systems. In the model, both the fish and phytoplankton populations are assumed to be growing logistically, the fish population is nonlinearly harvested, and the interaction between phytoplankton and zooplankton is described by the Crowley–Martin functional response. Stability analyses for the plankton–fish interaction model have been carried out for both non-spatial and spatial systems. The theoretical results are then supported by numerical simulations. In the case of non-spatial system, single-parameter bifurcation diagrams are used, while in the spatial system numerical simulations for one- and two-dimensional cases are performed. In the case of a non-spatial system, the conditions for the existence of a positive equilibrium point, as well as their local and global stability analyses, have been obtained. In the spatial system, the stability and existence of Hopf bifurcation have been discussed, and different conditions for Turing pattern information have been established through diffusion-driven instability analysis. Taken together, these results show that spatial heterogeneity, the mortality rate of phytoplankton, and the constant harvesting of the fish population play important roles in the dynamical behavior of the marine system. [ABSTRACT FROM AUTHOR]

• To understand transmission dynamics of malicious signals in WSN, an energy efficient e-epidemic delay model is proposed. • Malicious signals can be controlled, system stabilizes with small delay and exhibits oscillatory behavior for large delay. • Data packet and discrete delays are responsible for stability switching and occurrence of chaotic dynamics respectively. • Occurrence of double Hopf bifurcation indicates about regular functionality and robust security of sensor network. • We examine how the stability regions and bifurcation scenario changes with the transmission rate. An attempt has been made to understand the transmission dynamics of malicious signals in wireless sensor networks. An energy efficient e-epidemic model with data packet transmission delay has been considered. Linear stability analysis is performed for all the equilibrium points, whose characteristic equations involve the time delay. Global stability and Hopf bifurcation analyses are carried out for the endemic equilibrium point of the delay system. Attention has been paid to the direction of Hopf bifurcation and the stability of the resulting periodic solutions. Numerical study exhibits double Hopf bifurcation dynamics and it causes stability switching i.e., instability to stability and back to instability or the reverse transition of the solution of the considered system. Finally, numerical simulations provide useful observations for different delays and they show an interesting bifurcation scenario. The impact of the control parameters β and τ on the system dynamics have been investigated. Our results suggest that the data packet delay and discrete delay are responsible for the stability switching and the occurrence of chaotic dynamics respectively. The presence of chaotic dynamics indicates fragile security system of the network. Looking into the simulation results, we have indicated the most effective control measures to control the propagation of malicious signals. [ABSTRACT FROM AUTHOR]

Electrical activities of excitable cells produce diverse spiking-bursting patterns. The dynamics of the neuronal responses can be changed due to the variations of ionic concentrations between outside and inside the cell membrane. We investigate such type of spiking-bursting patterns under the effect of an electromagnetic induction on an excitable neuron model. The effect of electromagnetic induction across the membrane potential can be considered to analyze the collective behavior for signal processing. The paper addresses the issue of the electromagnetic flow on a modified Hindmarsh–Rose model (H–R) which preserves biophysical neurocomputational properties of a class of neuron models. The different types of firing activities such as square wave bursting, chattering, fast spiking, periodic spiking, mixed-mode oscillations etc. can be observed using different injected current stimulus. The improved version of the model includes more parameter sets and the multiple electrical activities are exhibited in different parameter regimes. We perform the bifurcation analysis analytically and numerically with respect to the key parameters which reveals the properties of the fast-slow system for neuronal responses. The firing activities can be suppressed/enhanced using the different external stimulus current and by allowing a noise induced current. To study the electrical activities of neural computation, the improved neuron model is suitable for further investigation. [ABSTRACT FROM AUTHOR]

The crux of present investigation is to develop an interval-valued population model for the interaction between phytoplankton, zooplankton and fish population under cyrtoid type functional response. The present study is also concerned to analyze the mathematical model under impreciseness and the parametric functional form for an interval valued model parameters. The boundedness, existence of the solution, stability analysis and all possible feasible equilibrium points have been examined. The optimal harvesting strategy has been implemented and obtained the optimal solution with the help of the Pontryagin maximum principle. The significant impact of interval valued biological parameters has been analyzed and portrayed by means of graph for given different fit values, approximate to the model system in real scenario. • An interval valued fuzzy model for interaction between plankton-fish population in marine ecosystem is developed mathematically. • Existence of the solutions and model stability analysis has been carried out. • Optimal harvesting strategy has been performed and obtained the optimal solutions with the help of Pontryagin maximum principal. • Time series analysis and phase portrait have been examined by means of graph. [ABSTRACT FROM AUTHOR]

In this paper, an attempt is made to understand the transmission dynamics of Ebola virus disease (EVD) incorporating fuzziness in all biological parameters due to its natural variability. To characterize the transmission trajectories of Ebola outbreak, we propose and analyze two SEIR and SEIRHD type transmission models. Using triangular fuzzy numbers for the imprecise parameters, we first study the existence of the equilibria and their stability. Both of the model have two equilibria, namely the disease-free and endemic. Stability of the disease-free and endemic equilibria is related with basic reproduction number that has been calculated from next generation matrix. Stability analysis of the system shows that the disease free equilibrium is locally as well as globally asymptotically stable when the basic reproduction number is less than unity. Under some additional conditions, the model system becomes locally asymptotically stable at unique endemic equilibrium when basic reproduction number is greater than unity. Finally, we perform some numerical experiments to justify the theoretical estimate. [ABSTRACT FROM AUTHOR]

Predator–prey interactions with stochastic forcing have been extensively investigated in the literature. However there are not many investigations of such models, that include prey defense. The goal of the current manuscript is to investigate a stochastic predator–prey model with mutual interference, and various Holling type functional responses, where the prey is able to release toxins as defense against a predator. This can also be generalized to include group or herd defense, toxin production and mimicry. We establish local and global existence for the stochastic model, and perform various numerical simulations to support our theoretical results. Our key result is that we have globally existing solutions independent of the magnitude of the toxin release parameter, or the predation rates. We also show that large enough noise intensity in solely the prey, can lead to extinction in the noisy model, for both species, whilst there is persistence in the deterministic model. [ABSTRACT FROM AUTHOR]

The control of highly contagious diseases is very important today. In this paper, we proposed an SEIR model with Crowley–Martin-type incidence rate and Holling type II and III treatment rates. Dynamics of the spread of infection and its control are performed for both the cases of treatment functions. We have performed the stability and bifurcation analyses of the model system. The sensitivity analysis of all the parameters with respect to the basic reproduction number has been performed. Furthermore, we discussed the optimal control strategy using Pontryagin's maximum principle and determined the effect of control parameter u on the model dynamics. Moreover, we validate the theoretical results using numerical simulations. Between both the treatment functions, we observe that the implementation of Holling type II treatment is most effective to prevent the spread of diseases. Thus, we conclude that the pervasive effect of treatment not only reduces the basic reproduction number as the control parameter u increases with nonlinear treatment, h(I) but also controls the spread of disease infection among the population. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Zhejiang University (Science Edition) is the property of Journal of Zhejiang University (Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we consider a Gause-type model system consisting of two prey and one predator. Gestation period is considered as the time delay for the conversion of both the prey and predator. Bobcats and their primary prey rabbits and squirrels, found in North America and southern Canada, are taken as an example of an ecological system. It has been observed that there are stability switches and the system becomes unstable due to the effect of time delay. Positive invariance, boundedness, and local stability analysis are studied for the model system. Conditions under which both delayed and nondelayed model systems remain globally stable are found. Criteria which guarantee the persistence of the delayed model system are derived. Conditions for the existence of Hopf bifurcation at the nonzero equilibrium point of the delayed model system are also obtained. Formulae for the direction, stability, and period of the bifurcating solution are conducted using the normal form theory and center manifold theorem. Numerical simulations have been shown to analyze the effect of each of the parameters considered in the formation of the model system on the dynamic behavior of the system. The findings are interesting from the application point of view. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an SLBRS computer virus model with time delay and impact of antivirus software. The proposed model considers the entering rates of all computers since every computer can enter or leave the Internet easily. It has been observed that there is a stability switch and the system becomes unstable due to the effect of the time delay. Conditions under which the system remains locally stable and Hopf bifurcation occurs are found. Sufficient conditions for global stability of endemic equilibrium are derived by constructing a Lyapunov function. Formulae for the direction, stability, and period of the bifurcating periodic solutions are conducted with the aid of the normal form theory and center manifold theorem. Numerical simulations are carried out to analyze the effect of some of the parameters in the system on the dynamic behavior of the system. [ABSTRACT FROM AUTHOR]

Salton Sea (a destination resort) is to be saved from being converted into a skeleton-filled wasteland. The critical amount of water flowing into the sea to maintain its level and salinity has been diverted since January 2018. This will lead to shrinking volumes and increasing salinities. Ecological consequences and public health impacts of altered conditions will be phenomenal. We design and analyze a minimal eco-epidemiological model to figure out future journey of this sea; a way station for fish-eating migratory birds. The mathematical model has been assembled in terms of prey-predator interaction. The salient feature of the proposed model is its seasonally varying contact rate which represents rate of conversion of susceptible fishes into infectives. We have analytically investigated the global stability, disease persistence and periodic solutions of the proposed model system. Susceptible prey-induced periodic solution is globally asymptotically stable when R ̄ 0 1 < 1 , otherwise unstable and hence disease persists for R ̄ 0 1 > 1. Global stability and Hopf bifurcation (HB) analysis help us extract parameter values to explore the dynamical behavior of the model system. Two-dimensional parameter scans and bifurcation diagrams reveal that the model displays propensity towards chaotic dynamics, which is associated with extinction-sized population densities. In the presence of stochastic external forces, this implies extinction of most of the fish species. This, in turn, suggests that resident birds will have to migrate to other destinations. The fish-eating migratory birds will be forced to switch over to invertebrates. Ecological consequences and public health impacts of this transition would be severe. Conservation groups are solicited to draw attention of the government to avert this impounding danger. It is important to plan for an ecosystem-wide transition such that impacts on birds and on human inhabitants living adjacent to the shrinking and salinizing sea are minimized. [ABSTRACT FROM AUTHOR]