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Two classes of optimal quaternary sequences have been constructed by applying the sign alternation transform and Gray mapping to Legendre sequence pair, twin-prime sequence pair and GMW sequence pair. In this paper, a new method for investigating the linear complexity over finite field is proposed, and the exact values of the linear complexity over finite field F 4 and Galois ring Z 4 of the quaternary sequences are determined. The results show that their linear complexity are quite good. [ABSTRACT FROM AUTHOR]

Therapeutic agents acting on RNA, including RNA modification, RNA editing and RNA interference (RNAi), play a vital role in gene function study, signaling pathway, drug discovery, disease treatment, vaccine development and so on. Therein, RNAi as an emerging gene therapy has been widely applied in many cancer studies by silencing oncogenes or specific mRNA in malignant tumor cells. Mechanism and efficiency of RNAi are the key issues of RNAi technology. RNA silencing involves dynamic modeling, analyses and optimal control of RNAi gene system. Physiological delay and Hill response describing off-target are considerable elements involving RNAi efficiency. In this paper, we first formulate a four-dimensional RNAi model with time delays and Hill functions, and then investigate the complex dynamic behaviors including the number, existence and stability of internal equilibria and Hopf bifurcations of single delay and two delays. Furthermore, based on the specific mRNA degradation adopted in impulsive patterns, we build an optimal problem by adding exogenous dsRNA at alterable time points in variable dosages in a treatment session. By the method of gradient formula, we can find the optimal impulsive time and proportion of dsRNA. Finally, simulation indicates that (1) physiological lags not only raise the oscillations of mRNA but also cut down the levels of cost; (2) smaller delays and larger rates of siRNA–mRNA complex formation and dsRNA synthesis imply the rapid composition of RISC and fast synthesis of dsRNA leading to more desirable therapeutic schedule, which affords evidence for gene regulation and RNAi; (3) a larger half-saturation coefficient characterizes a unique and stable higher targeted mRNA, whereas a smaller half-saturation coefficient generates bistability in which the higher and lower targeted mRNAs simultaneously emerge; and (4) the bistability will provide a good guidance to control, suppress and degrade targeted mRNA. [ABSTRACT FROM AUTHOR]

Polyimide (PI) nanofibrous aerogels (NFAs) have garnered significant attention for their exceptional mechanical and thermal properties, making them promising materials for heat insulation applications. However, there is a lack of comprehensive research on heat transfer of PI NFAs on the modeling and prediction. Therefore, three modified unit cells with the features of PI NFA backbone were constructed for the finite element simulation. Subsequently, the comparisons of our results with experimental data from available literature were conducted. It indicated that the cubic unit cell fitted well with the experimental values when the density was lower than 50 kg / m 3 , while the Weaire–Phelan unit cell demonstrated good agreement when the density was higher than 50 kg / m 3 . A series of parametric studies were performed and indicated that the thermal conductivity is proportional to the nanofiber diameter, whereas inversely proportional to the pore size and porosity. Our research will provide novel insights to the selection of parameters for industrial manufacturing of thermal insulation materials in aerospace, energy, protection, etc. [ABSTRACT FROM AUTHOR]

Intermittent androgen suppression in the prostate cancer is often relapsed by the increasing of prostate specific antigen level during the on-treatment. Historically, chemotherapy has had a limited role in the treatment of prostate cancer. However, new agents are showing promise in patients with advanced disease. Intermittent androgen suppression plus chemotherapy in pulsed pattern has become an indispensable clinical scheme for prostate cancer, which is presented to describe the transformation mechanism for three kinds of cancer cells in this paper. The model is then extended to include the residual effect of chemotherapy which suppresses the cancer cells production, thereby preventing the relapse. The optimal controls represent the efficiencies of both intermittent androgen suppression and chemotherapy in suppressing relapse of prostate cancer. Based on an optimal algorithm, numerical simulations are implemented not only to show the optimal durations of on- and off-treatment and chemotherapy dosages but also to present the effectiveness of different strategies in inhibiting the relapse for three types of patients. Results reveal that the optimal intermittent androgen suppression scheme with alterable treatment cycles is pivotal for type I and II patients, in part because it can greatly reduce the on-treatment time and degrade the level of prostate specific antigen. Furthermore, optimal hybrid schedule even averts the relapse of prostate cancer for type II and III patients. Finally, comparing the prostate specific antigen under intermittent androgen suppression schedule with residual effect of chemotherapy to one without residual effect of chemotherapy demonstrates the validity of both our model and algorithms in lessening the prostate specific antigen and decreasing the chemotherapy dosages. [ABSTRACT FROM AUTHOR]

Identifying proteins is crucial for disease diagnosis and treatment. With the increase of known proteins, large-scale batch predictions are essential. However, traditional biological experiments being time-consuming and expensive are difficult to accomplish this task efficiently. Nevertheless, deep learning algorithms based on big data analysis have manifested potential in this aspect. In recent years, language representation models, especially BERT, have made significant advancements in natural language processing. In this paper, using three protein segmentation methods and three encoder numbers, nine BERT models with different sizes are constructed to predict whether known proteins are DNA-binding proteins or not. Furthermore, based on the concept of protein motifs, multi-scale convolutional networks are fused into the models to extract the local features of DNA-binding proteins. Finally, we find that the larger the number of encoders, the better the model predictions under the condition of considering each amino acid in the protein as a word. Our proposed algorithm achieves 81.88% sensitivity and 0.39 MCC value on the test set. Furthermore, it achieves 62.41% accuracy on the independent test set PDB2272. It is evident that our proposed method can be a tool to assist in the identification of DNA-binding proteins. [ABSTRACT FROM AUTHOR]

Approximate Bayesian Computation algorithms (ABC), bypassing the intractable likelihood function, are commonly used to estimate the posterior distributions of parameters in practice. However ABC algorithms also have some inherent problems in the application, for example, when the algorithm maintains operating efficiency, it is difficult to obtain a more accurate approximation of the target distribution. To overcome these defects, an improved ABC algorithm is introduced in this article. The novel algorithm based on the ABC Sequential Monte Carlo (ABC-SMC) and a new recalibration post-processing methods is obtained to estimate the parameters of the biodynamic models, which is also called the ABC-SMCR algorithm. Through this article, it will be shown that the new algorithm is promising in processing the parameter inference problem. This algorithm not only offers high computational efficiency but also improves the quality estimate of the posterior distributions. To demonstrate its strengths, two examples are given. The first illustrative example on the basis of simulated data mainly demonstrates that it can be used to obtain accurate parameter inference of the Lotka-Volterra model. The second illustration based on actual flu outbreak data are given to show the computational efficiency of this algorithm in parameter estimation of the epidemic model. [ABSTRACT FROM AUTHOR]

Model selection and parameter estimation are very important in many fields. However, the existing methods have many problems, such as low efficiency in model selection and inaccuracy in parameter estimation. In this study, we proposed a new algorithm named improved approximate Bayesian computation sequential Monte Carlo algorithm (IABC-SMC) based on approximate Bayesian computation sequential Monte Carlo algorithm (ABC-SMC). Using the IABC-SMC algorithm, given data and the set of two models including logistic and Gompertz models of infectious diseases, we obtained the best fitting model and the values of unknown parameters of the corresponding model. The simulation results showed that the IABC-SMC algorithm can quickly and accurately select a model that best matches the corresponding epidemic data among multiple candidate models and estimate the values of unknown parameters of model very accurately. We further compared the effects of IABC-SMC algorithm with that of ABC-SMC algorithm. Simulations showed that the IABC-SMC algorithm can improve the accuracy of estimated parameter values and the speed of model selection and also avoid the shortage of ABC-SMC algorithm. This study suggests that the IABC-SMC algorithm can be seen as a promising method for model selection and parameter estimation. [ABSTRACT FROM AUTHOR]

Computer worms are serious threats to Internet security and have caused billions of dollars of economic losses during the past decades. In this study, we implemented a susceptible–infected–recovered–dead (SIRD) model of computer worms and analyzed the characteristics and mechanisms of worm transmission. We applied the ordinary differential equation model to simulate the transmission process of computer worms and estimated the unknown parameters of the SIRD model through the methods of least squares, Markov chain Monte Carlo, and ensemble Kalman filtering (ENKF). The results reveal that the proposed SIRD model is more accurate than the susceptible–exposed–infected–recovered–susceptible model with respect to parameter estimation. [ABSTRACT FROM AUTHOR]

Considering the mature condition of any individual to have eaten a specific amount of food during the entire period that it can spend at its immature stage, we propose a size-structured model by a first-order quasi-linear partial differential equation. The model can be firstly reduced to a single state-dependent delay differential equation and then to a constant delay differential equation. The state-dependent delay represents intra-specific competition among individuals for limited food resources. A complete analysis of the global dynamics on the positivity and boundedness of solutions, global stability for each equilibrium and Hopf bifurcation is carried out. Our results imply that the delay leads to instability that is shown by a simple example of a certain structured population model. [ABSTRACT FROM AUTHOR]

Excessive accumulation of β − c a t e n i n proteins is a vital driver in the development of breast cancer. Many clinical assessments incorporating immunotherapy with targeted mRNA of β − c a t e n i n are costly endeavor. This paper develops novel mathematical models for different treatments by invoking available clinical data to calibrate models, along with the selection and evaluation of therapy strategies in a faster manner with lower cost. Firstly, in order to explore the interactions between cancer cells and the immune system within the tumor microenvironment, we construct different types of breast cancer treatment models based on RNA interference technique and immune checkpoint inhibitors, which have been proved to be an effective combined therapy in pre-clinical trials associated with the inhibition of β − c a t e n i n proteins to enhance intrinsic anti-tumor immune response. Secondly, various techniques including MCMC are adopted to estimate multiple parameters and thus simulations in agreement with experimental results sustain the validity of our models. Furthermore, the gradient descent method and particle swarm algorithm are designed to optimize therapy schemes to inhibit the growth of tumor and lower the treatment cost. Considering the mechanisms of drug resistance in vivo, simulations exhibit that therapies are ineffective resulting in cancer relapse in the prolonged time. For this reason, parametric sensitivity analysis sheds light on the choice of new treatments which indicate that, in addition to inhibiting β − c a t e n i n proteins and improving self-immunity, the injection of dendritic cells promoting immunity may provide a novel vision for the future of cancer treatment. Overall, our study provides witness of principle from a mathematical perspective to guide clinical trials and the selection of treatment regimens. • Mathematical model with synergetic effects of RNAi and Anti-PD-1 is formulated.. • Optimal therapy schemes are designed by means of two kinds of algorithms. • Long-term treatment leading to drug resistance gives rise to cancer recurrence. • Parametric sensitivity reveals the role of β − c a t e n i n in the progress of cancer. • Mature dendritic cells have great potential as a new anti-tumor strategy. [ABSTRACT FROM AUTHOR]

In this paper, the stability properties of a parabolic partial differential equation with state-dependent delay are investigated by the heuristic approach. The previous works [1,2] obtained a continuously differentiable semiflow with continuously differentiable solution operators defined by the classical solutions, and resolved the problem of linearization for this equation. Here, we clarify the relation between the spectral properties of the linearization of the semiflow at a stationary solution and the strong continuous semigroup defined by the solutions of the linearization of this equation, and consider the local stable and unstable invariant manifolds of the semiflow at a stationary solution. By a biological application, we finally verify all hypotheses for an age structured diffusive model with state-dependent delay and consider its stability behavior. [ABSTRACT FROM AUTHOR]

Sex pheromone, aiming at mating disruption (MD), being species specific and leaving no toxic residues in the produce grown, offers an attractive alternative to conventional pesticides. In this paper, by incorporating the gestation delay and sex pheromone, we explore the impact of MD control on the dynamic behaviors of pest system. Firstly, the boundness, stability and bifurcation of system are deliberated. Secondly, an optimal control problem based on sex pheromone and pesticide is transformed into an equivalent optimal parameter selection problem by introducing the constrain violation function. Additionally, the gradients of the cost function with respect to the dose of sex pheromone and the killing rate are given. Furthermore, simulations are executed to validate the validity of our method. Meanwhile, our results indicate that gestation delay increases the extinction risk of the population and liberating sex pheromone destroys the stability of equilibrium states. [ABSTRACT FROM AUTHOR]

Background: As a highly efficient and specific gene regulation technology, RNAi has broad application fields and good prospects. The effect of RNAi enhances as the dosage of siRNA increases, while an exorbitant siRNA dosage will inhibit the RNAi effect. So it is crucial to formulate a dose-effect model to describe the degradation effects of the target mRNA at different siRNA dosages. Results: In this work, a simple RNA interference model with hill kinetic function (Giulia Cuccato et al. (2011)) is extended. Firstly, by introducing both the degradation time delay τ1 of mRNA caused by siRNA and the transportation time delay τ2 of mRNA from the nucleus to the cytoplasm during protein translation, one acquires a novel delay differential equations (DDEs) model with physiology lags. Secondly, qualitative analyses are executed to identify regions of stability of the positive equilibrium and to determine the corresponding parameter scales. Next, the approximate period of the limit cycle at Hopf bifurcation points is computed. Furthermore we analyze the parameter sensitivity of the limit cycle. Finally, we propose an optimal strategy to select siRNA dosage which arouses significant silencing efficiency. Conclusions: Our researches indicate that when the dosage of siRNA is large, oscillating periods are identical for disparate number of siRNA target sites even if it greatly impacts the critical siRNA dosage which is the switch of oscillating behavior. Furthermore, parametric sensitivity analyses of limit cycle disclose that both of degradation lag and maximum degradation rate of mRNA due to RNAi are principal elements on determining periodic oscillation. Our explorations will provide evidence for gene regulation and RNAi. [ABSTRACT FROM AUTHOR]

Abstract Considering planktonic ecosystem as the bottom trophic levels of aquatic food webs, we derive a nutrient–phytoplankton–zooplankton model with spatially averaged parameters, where zooplankton population with two age classes and a fixed maturation period lives in a spatially bounded environment. The model can be transformed into a reaction–diffusion equation with non-local delay. Such transformation allows us to use results readily available from comparison argument and persistence theory to study the global compact attractor of solution semiflow, global attractivity and globally asymptotical stability of steady states. Our results can be used to design the control strategy of harmful algal blooms which have caused large fish kills and millions of dollars in economic losses. [ABSTRACT FROM AUTHOR]

Aphids, the sap-sucking insects, often feeding in clusters on new plant growth, have resulted in large amounts of resources and efforts being spent attempting to control their activities. Taking cotton aphids as an example, this paper presents optimal control problems governed by stochastic models with impulsive interferences. Differing from the moment closure equation methods which are computationally intractable when the model contains excessive species, a new computational approach is employed to solve this problem. The key of the approach is to establish a functional relationship between the control variables involving the releasing rates of sterile insects and the spraying rates of pesticide and corresponding states on aphids and sterile aphids. Then the log-linear regression model is proposed to link the control variables with the moments (including the mean and variance) of states. Using training sample simulated from Gillespie algorithm, the regression coefficients for constraints and the objective function are estimated by least squares method. Simulation shows the error of the prediction of this model is relatively low and control results based on regression model are superior to the method based on the moment closure equations in terms of the control cost. Finally, the relative impacts of the prices and area of the field on optimal tactics are explored. [ABSTRACT FROM AUTHOR]

Media coverage reduces the transmission rate from infective to susceptible individuals and is reflected by suitable nonlinear functions in mathematical modeling of the disease. We here focus on estimating the parameters in the transmission rate based on a stochastic SIR epidemic model with media coverage. In order to reduce the computational load, the Newton-Raphson algorithm and Markov Chain Monte Carlo (MCMC) technique are incorporated with maximum likelihood estimation. Simulations validate our estimation results and the necessity of a model with media coverage when modeling the contagious diseases. [ABSTRACT FROM AUTHOR]

This paper focuses on asymptotic mean-square boundedness of several numerical methods applied to a class of stochastic age-dependent population equations with Poisson jumps. The conditions under which the underlying systems are asymptotic mean-square boundedness are considered. It is shown that the asymptotic mean-square boundedness is preserved by the compensated split-step backward Euler method and compensated backward Euler method without any restriction on stepsize, while the split-step backward Euler method and backward Euler method could reproduce asymptotic mean-square boundedness under a stepsize constraint. The results indicate that compensated numerical methods achieve superiority over non-compensated numerical methods in terms of asymptotic mean-square boundedness. Finally, an example is given for illustration. [ABSTRACT FROM AUTHOR]

A state dependent impulsive control model is proposed to model the spread of computer virus incorporating media coverage. By the successor function, the sufficient conditions for the existence and uniqueness of order-1 periodic solution are presented first. Secondly, for two classes of periodic solutions, the geometric property of successor function and the analogue of the Poincaré criterion are employed to obtain the stability results. These results show that the number of the infective computers is under the threshold all the time. Finally, the theoretic and numerical analysis show that media coverage can delay the spread of computer virus. [ABSTRACT FROM AUTHOR]

We propose and study a predator-prey model with state-dependent delay where the prey population is assumed to have an age structure. The state-dependent delay appears due to the mature condition that the prey must spend an amount of time in the immature stage sufficient to accumulate a threshold amount of food. We perform a qualitative analysis of the solutions, which includes studying positivity and boundedness, existence and local stability of equilibria. For the global dynamics of the system, we discuss an attracting region which is determined by solutions, and the region collapses to the interior equilibrium in the constant delay case. [ABSTRACT FROM AUTHOR]

This paper mainly provides Hopf bifurcation formulas for a general Gause type predator–prey system with diffusion and Neumann boundary condition by using the center manifold theory and normal form method, where the spectral and stability analysis around an equilibrium is addressed, and our results can be applied to the case without diffusion. As an application of these results, we give a complete and rigorous analysis of the global dynamics of a diffusive predator–prey model with herd behavior, especially, the Hopf bifurcation and its direction, and the stability of the bifurcating periodic solutions. [ABSTRACT FROM AUTHOR]

Yongzhen et al. (2010) describe a mathematical model of a scenario where a plant population is imported to a pest–predator system with an infected pest. Thus a plant–pest–predator eco-epidemiological model disturbed by an impulsive effect is proposed. First of all, the stability conditions of the susceptible pest-eradication periodic solution for eradicating the susceptible pest are investigated. Compared with the results in (Yongzhen et al., 2010), the presence of the plant population increases the cost of natural enemies as well as the demand for insecticide. In addition, we study the effect of the death rate of the infected pest on pest control in terms of evolution of virulence and the basic reproductive number. Results show that larger mortalities of the infected pest will lead to the frustrated invasion or the instability of susceptible pest-eradication periodic solutions. Next, we focus on the four kinds of optimal impulsive control strategies, biological control, chemical control, and integrated control with fixed period or variable period, to maximize the yields of plants at the terminal time with minimum efforts. All the optimal control problems are solved via a time scaling technique and a gradient-based optimization method. Our results show that two parameters, the amount of sprayed infective pest and the kill fraction of the susceptible pest, play a key role in improving the yield of the plants. In addition, for the four kinds of control strategies, our results also show that biological control is more effective than chemical control to achieve an optimal solution, and the last two strategies can produce higher yields than the first two control strategies. [ABSTRACT FROM AUTHOR]

Based on literature [J. Q. Li, Z. E. Ma and F. Q. Zhang, Stability analysis for an epidemic model with stage structure, J. Appl. Math. Comput. 9 (2008) 1672-1679], incorporating the recovery of the infected population with the length of the infectious periods, a modified epidemic disease SIS model with delay and stage was investigated. First, the criteria keeping stability with delay were given. Next, in order to lower the level of the infected individuals and minimize the cost of treatment, mixed, early and late therapeutic strategies were introduced into our model, respectively. Then we investigated the existence and uniqueness of optimal controls. And then, we expressed the unique optimal control in terms of the solution of the optimality systems. Finally, by numerical simulations, several important results were acquired: (1) The terminal time influenced the early optimal control largely. In detail, for a shorter terminal time it was optimal to initiate treatment with maximal effort at the start of the epidemic and continue treatment with maximal effort until the switch time was arrived. But for a longer terminal time, the maximal treatment effort need not be a prerequisite at the start or end of the epidemic but it was obligatory at the metaphase of the epidemic. (2) For our SIS model, minimizing the total infectious burden of the disease can be achieved by only early optimal treatment tactics. (3) For a disease with a shorter infectious period time, more cost would be spent to control the disease in order to achieve the optimal control objective. Otherwise, a relative lower cost would be to control the disease with a longer infectious period. [ABSTRACT FROM AUTHOR]

In pest control, taking the lag of parasitic eggs, the lag effect of pesticide poisoning and the age of releasing natural enemies as control variables, combined with the crop fertility cycle, researches on the optimization problem of pest control models at seedling stage, the bud stage, and filling stage of crops fill in a gap. For these purposes, a generalized hybrid optimization problem involving state delay with characteristic times and parameter control is presented. Then an algorithm based on a gradient computation is given. Finally, two examples in an agroecological system are given to exhibit the effectiveness of the proposed optimization algorithm. [ABSTRACT FROM AUTHOR]

Abstract: Taking into account periodic impulsive biological and chemical control for pest management at different fixed moment, a three species prey–predator system with Holling type II functional response was investigated. By using Floquet’s theory and the small amplitude perturbation method, it was obtained that there exists an asymptotically stable preys-eradication periodic solution when the impulsive period is less than some critical minimum value (or the release amount of the predator is larger than some critical maximum value), and the system is permanent under the conditions that both the insecticidal effect and impulsive period are grater than some critical maximum values. Furthermore, it is obtained that IPM is more effective than any single one after comparison. Finally, numerical simulations are carried on to show the complex dynamic behavior of system. [Copyright &y& Elsevier]

Abstract: Considering the impact of harvesting on the coexistence and competitive exclusion of competitive predators, a two-zooplankton one-phytoplankton model with harvesting is proposed and investigated. First, stability criteria of the model is analyzed both from local and global point of view. Second, two types of zooplankton will competitively exclude each other in the absence of harvesting with the zooplankton with the larger threshold persisting. If harvest rates are discriminate, then a dominant zooplankton may occur depending on the harvesting level. Thus, for some harvesting levels, the zooplankton one may persist while for other harvesting levels zooplankton two may persist. Furthermore, the value of the harvesting level and coexistence line are obtained when coexistence occur. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings. [Copyright &y& Elsevier]

Abstract: Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation 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 equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, two SIR epidemic models with different patterns of recruitment and difference in immunity are investigated. When the recruitment rate is less than some threshold value, the disease will be eradicated. Furthermore, for the continuous recruitment model, according to the Poincare–Bendixson theorem, the global asymptotical stability of a unique positive equilibrium is obtained. For the pulse recruitment model, we investigated the existence of nontrivial periodic solutions via a supercritical (subcritical) bifurcation. From a biological point of view, our results indicate that (1) the disease can be eradicated if the recruitment rate is controlled under some threshold; (2) the number of the infected increases as the difference in immunity increases; (3) fewer individuals are infected as the pulse recruitment is taken, displaying its effect on the control of the disease. [Copyright &y& Elsevier]

Abstract: In this paper, two integrated pest management models are investigated, which rely on release of infective pest individuals and of natural enemies in a constant amount, together with spraying of pesticides. It is proved that the susceptible pests can be eradicated if the release amount of infected pests is above some threshold or the pesticide effect is above another threshold. Furthermore, permanent conditions are established when an impulsive control is used. Finally, numerical results show that (1) fewer infected pests or pesticides are needed as the impulsive strategy is taken, displaying its positive effect on the pest control; (2) our assumption that the natural enemies of the pests do not catch the infective pests would reduce the level of the susceptible pests. [Copyright &y& Elsevier]

In an ecosystem some populations not only consume the resource but also contribute themselves to the resource after senescence and other deaths and considered another source of resource. In view of these facts and based on whether the population individual is capable of reproduction, a single-species chemostat model with age structure and the contribution to resource is formulated and analyzed. We introduce two thresholds $${{\Re}_0}$$ and α0 by the method of next generation matrix and further obtain conditions of stability for equilibria. Our results indicate that the population can be eradicated if the input concentration of external resource α is controlled under a threshold α0. In addition, the results show that the contribution of population to resource make threshold value α0 larger, which implies, in view of the biological meaning, that such contribution plays a negative role in suppressing population. [ABSTRACT FROM AUTHOR]

Abstract: A delayed SEIQR epidemic model with pulse vaccination and the quarantine measure is investigated. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact periodic disease-free solution. Using the comparison method, we prove that the disease-free periodic solution is globally attractive when the basic reproductive number () is less than unity, and that the disease is permanent when another basic reproductive number () is greater than unity. In other words, the disease will be extinct if the pulse vaccination rate is larger than a critical value and the disease will be uniformly persistent if the vaccination rate is less than another critical value . Our results indicate that a longer latent period of the disease or a larger pulse vaccination rate will lead to the eradication of the disease, and whether the disease will be extinct or not is independent of the removal rate from the quarantined group. Furthermore, a larger fraction of susceptibles should be vaccinated against the disease unless the quarantine measure is taken. Finally, we find that the number of the infected decreases as the quarantine measure is taken. We carry out numerical simulations to verify our results. [Copyright &y& Elsevier]

Abstract: An impulsive delayed SI model with variable coefficients and a nonlinear incidence is formulated and analyzed. By introducing three thresholds, we obtain sufficient conditions for eradication and permanence of the disease, respectively. It is shown that the conditions depend on time delay for both the global attractivity of the positive infection-free periodic solution and permanence of the model. Furthermore, our results indicate that the disease will disappear if the ratio of the maximum to minimum of the pulse vaccination rate is lager than some value. The main feature of this paper is that we introduce multi-delays and variable coefficients into the SI model, and exhibit a new method which is applied to investigate this model. Numerical results show that the system we considered has complex dynamics including periodic and quasi-periodic oscillations. [Copyright &y& Elsevier]

Abstract: Three different vaccination and treatment strategies in the SIR epidemic model with saturated infectious force and vertical transmission are analyzed. The dynamics of epidemic models are globally investigated by using Floquet theory and comparison theorem of impulsive differential equation. Thresholds are identified and global stability results are proved. For every treatment and vaccination strategy, the disease-free periodic solution of impulsive system has been obtained and is found to be globally asymptotically stable when the basic reproduction number is less than one, equivalently the cure rate is larger than the threshold value, whereas the disease is persistent when the basic reproduction number is larger than one. These results indicate that a large cure rate will lead to the eradication of a disease. [Copyright &y& Elsevier]

This paper deals with a general age-structured model with diffusion. The existence and uniqueness of solutions of the equivalent integral equation are obtained in light of the contraction mapping theorem. By taking the mosquito population growth as a motivating example, we derive a periodic stage-structured model with diffusion, intra-specific competition and periodic delay. Next, we show that the solution is globally bounded for the setup we chose. Then, the basic reproduction number R 0 for this model is introduced to establish the threshold dynamics on mosquito extinction and persistence in terms of R 0. In the case where intra-specific competition among immature individuals is ignored, the adult equation is decoupled from the full equations, and the global stability of the positive periodic solution is then obtained by introducing a suitable phase space on which the periodic semiflow is eventually strongly monotone and strictly subhomogeneous. [ABSTRACT FROM AUTHOR]

In this work, we consider a logistic fishery model and discuss the selective impulsive harvesting of fish above a certain age or size by incorporating a time delay in the impulsive harvesting term. It is proved that there exists an asymptotically stable positive periodic solution $x^*_{l1}(t)$ when the catchability coefficient h is less than some critical value $h^*_{l}$. It is concluded that $h^*_{l}$ and $x^*_{l1}$ are increasing with respect to l. Simulations shows that the delayed harvesting is advantageous to the sustainability of the population. [ABSTRACT FROM AUTHOR]

This work investigates the dynamic behaviors of one-prey multi-predator model with defensive ability of the prey by introducing impulsive biological control strategy. By using the Floquent theorem and the small amplitude perturbation method, it is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value, and a permanence condition is established via the method of comparison involving multiple Liapunov functions. It is shown that the multi-predator impulsive control strategy is more effective than the classical one and makes the behavior dynamics of the system more complex. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, one investigates the dynamic behaviors of one-prey multi-predator model with Holling type II functional response by introducing impulsive biological control strategy (periodic releasing natural enemies at different fixed time). By using Floquet theorem and small amplitude perturbation method, it is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value and permanence condition is established via the method of comparison involving multiple Liapunov functions. It is shown that multi-predator impulsive control strategy is more effective than the classical and single one. [Copyright &y& Elsevier]

This paper defines a new scoring rule, namely relative model score (RMS), for evaluating ensemble simulations of environmental models. RMS implicitly incorporates the measures of ensemble mean accuracy, prediction interval precision, and prediction interval reliability for evaluating the overall model predictive performance. RMS is numerically evaluated from the probability density functions of ensemble simulations given by individual models or several models via model averaging. We demonstrate the advantages of using RMS through an example of soil respiration modeling. The example considers two alternative models with different fidelity, and for each model Bayesian inverse modeling is conducted using two different likelihood functions. This gives four single-model ensembles of model simulations. For each likelihood function, Bayesian model averaging is applied to the ensemble simulations of the two models, resulting in two multi-model prediction ensembles. Predictive performance for these ensembles is evaluated using various scoring rules. Results show that RMS outperforms the commonly used scoring rules of log-score, pseudo Bayes factor based on Bayesian model evidence (BME), and continuous ranked probability score (CRPS). RMS avoids the problem of rounding error specific to log-score. Being applicable to any likelihood functions, RMS has broader applicability than BME that is only applicable to the same likelihood function of multiple models. By directly considering the relative score of candidate models at each cross-validation datum, RMS results in more plausible model ranking than CRPS. Therefore, RMS is considered as a robust scoring rule for evaluating predictive performance of single-model and multi-model prediction ensembles. [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]

This article deals with a stage-structured model with state-dependent delay which is assumed to be an increasing function of the population density with lower and upper bound. Firstly, according to the principle of linearized stability (Theorem 3.6, Hartung et al. in Handbook of differential equations: ordinary differential equations, 2006), we study the local stability of system in combination with the positivity and boundedness of solutions. By using the comparison principle obtained and an iterative method, the global stability of the equilibria is completely analyzed. Our results show how the interaction between interspecific and intraspecific competition affects the coexistence of both species. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a numerical method preserving positivity for stochastic age-dependent population equations. We use the balanced implicit numerical techniques to maintain the nonnegative path of the exact solution. It is proved that the Balanced Implicit Method (BIM) preserves positivity and converges with strong order 1/2 under given conditions. Finally, two examples are simulated to verify the positivity and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Considering many species can release toxic substances to protect themselves against predators, a diffusive predator and toxic prey system with spatial heterogeneity in predator and prey populations has been investigated. For this system, we give a complete and rigorous analysis of the global dynamics with the boundedness, globally asymptotical stability, transcritical bifurcation, Hopf bifurcation and its direction, and the stability of the bifurcating periodic solutions. Meanwhile, we consider the effects of toxins produced by the prey on the dynamic behavior. The consequence of the global stability of the coexistence equilibrium is that the toxin’s intrinsic characteristic will not change the stability of the system irreversibly. Our results show that the toxin-produced by the prey (phytoplankton) may be used as a bio-control agent for the Harmful Algal Bloom problems. [ABSTRACT FROM AUTHOR]

In this paper, the smoothness properties of semiflows on C 1 -solution submanifold of a parabolic partial differential equations with state-dependent delay are investigated. The problem is formulated as an abstract ordinary retarded functional differential equation of the form d u ( t ) / d t = A u ( t ) + F ( u t ) with a continuously differentiable map G from an open subset U of the space C 1 ( [ − h , 0 ] , L 2 ( Ω ) ) , where A is the infinitesimal generator of a compact C 0 -semigroup. The present study is continuation of a previous work [14] that highlights the classical solutions and C 1 -smoothness of solution manifold. Here, we further prove the continuous differentiability of the semiflow. We finally verify all hypotheses by a biological example which describes a stage structured diffusive model where the delay, which is the time taken from birth to maturity, is assumed as a function of a immature species population. [ABSTRACT FROM AUTHOR]

In this paper, a new split-step θ (SS θ ) method for stochastic age-dependent population equations with Poisson jumps is constructed. The main aim of this paper is to investigate the convergence of the SS θ method for stochastic age-dependent population equations with Poisson jumps. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from theory, the results show that the SS θ method has better accuracy compared to the Euler method. [ABSTRACT FROM AUTHOR]

By studying an infection-age structured model, we consider the effects of releasing sterile males and the fertility of infected mosquitoes on the mosquito-borne diseases transmission including the extinction of mosquitoes, the elimination and persistence of diseases. Firstly, equivalent integral equations are established to prove the well-posedness of solutions. Then, the main results of disease dynamics are given. By taking chikungunya as a numerical simulation example, an optimal releasing threshold is given according to our presupposed control standard. When the fertility disturbance of infected mosquitoes is small, the high releasing amount plays a main role on the control of the disease; however, when the fertility disturbance is large, the initial distributions and the fertility of infected mosquitoes are the key factors to control the disease. Mathematically, the fertility of infected mosquitoes makes the system have complex dynamics with multiple positive equilibria and bistability. [ABSTRACT FROM AUTHOR]

Abstract: In compared with specialist predators which feed almost exclusively on a specific species of prey, generalist predators feed on many types of species. Consequently, their dynamics is not coupled to the dynamics of a specific prey population, and the generalist predators has itself growth function which be extended a well-known logistic growth term. We develop a generalist predator–prey model with diffusion and study the effect of harvesting and delay under Neumann conditions. The stability of the equilibria is firstly investigated, and the existence of traveling wave solutions is then established by constructing a pair of upper–lower solutions and using the cross iteration method and Schauder’s fixed point theorem. [Copyright &y& Elsevier]

Abstract: This paper deals with a predator–prey model with specialist harvesting, representing a two predators (Zooplankton) and one resource (Phytoplankton) system. First, the existence and stability of equilibria is analyzed both from local and global point of view. Our results indicate that a specialist harvesting which is discriminate may mediate the coexistence of the two zooplankton species which competitively exclude each other in absence harvesting. Although in most cases increasing harvesting reduces the two zooplankton species numbers, when harvesting leads to coexistence, it may also lead to increase the two zooplankton species numbers. Furthermore, to protect fish population from over exploitation a control instrument tax is imposed. The problem of optimal taxation policy is then solved by using Pontryagin’s maximal principle. It is established that the zero discounting leads to the maximization of the net economic revenue to the society and an infinite discount rate leads to complete dissipation of the net economic revenue to the society. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings. [Copyright &y& Elsevier]