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A delayed reaction-diffusion system with free boundaries is investigated in this paper to understand how the bacteria spread spatially to larger area from the initial infected habitat. Under the assumptions that the nonlinearities are of monostable type and the initial values satisfy some compatible condition, we show that the free boundary problem is well-posed and discuss the long-time behaviour of solution (including spreading and vanishing) in terms of the spatial-temporal risk index. Furthermore, to determine the spreading speed of free boundaries when spreading occurs, we first study the distribution of roots of a transcendental equation containing a polynomial of degree four and then establish the existence and uniqueness of monotone solution to a delay-induced nonlocal semi-wave problem by employing the approximation method, lower-upper solutions technique and Schauder fixed point theorem. It is shown that time delays slow down the spreading of bacteria. [ABSTRACT FROM AUTHOR]

Background: Radio/chemotherapy and immune systems provide examples of hormesis, as tumours can be stimulated (or reduced) at low radio/chemical or antibody doses but inhibited (or stimulated) by high doses. Methods: Interactions between effector cells, tumour cells and cytokines with pulsed radio/chemo-immunotherapy were modelled using a pulse differential system. Results: Our results show that radio/chemotherapy (dose) response curves (RCRC) and/or immune response curves (IRC) or a combination of both, undergo homeostatic changes or catastrophic shifts revealing hormesis in many parameter regions. Some mixed response curves had multiple humps, posing challenges for interpretation of clinical trials and experimental design, due to a fuzzy region between an hormetic zone and the toxic threshold. Mixed response curves from two parameter bifurcation analyses demonstrated that low-dose radio/chemotherapy and strong immunotherapy counteract side-effects of radio/chemotherapy on effector cells and cytokines and stimulate effects of immunotherapy on tumour growth. The implications for clinical applications were confirmed by good fits to our model of RCRC and IRC data. Conclusions: The combination of low-dose radio/chemotherapy and high-dose immunotherapy is very effective for many solid tumours. The net benefit and synergistic effect of combined therapy is conducive to the treatment and inhibition of tumour cells. [ABSTRACT FROM AUTHOR]

During the COVID-19 pandemic, control measures, especially massive contact tracing following prompt quarantine and isolation, play an important role in mitigating the disease spread, and quantifying the dynamic contact rate and quarantine rate and estimate their impacts remain challenging. To precisely quantify the intensity of interventions, we develop the mechanism of physics-informed neural network (PINN) to propose the extended transmission-dynamics-informed neural network (TDINN) algorithm by combining scattered observational data with deep learning and epidemic models. The TDINN algorithm can not only avoid assuming the specific rate functions in advance but also make neural networks follow the rules of epidemic systems in the process of learning. We show that the proposed algorithm can fit the multi-source epidemic data in Xi'an, Guangzhou and Yangzhou cities well, and moreover reconstruct the epidemic development trend in Hainan and Xinjiang with incomplete reported data. We inferred the temporal evolution patterns of contact/quarantine rates, selected the best combination from the family of functions to accurately simulate the contact/quarantine time series learned by TDINN algorithm, and consequently reconstructed the epidemic process. The selected rate functions based on the time series inferred by deep learning have epidemiologically reasonable meanings. In addition, the proposed TDINN algorithm has also been verified by COVID-19 epidemic data with multiple waves in Liaoning province and shows good performance. We find the significant fluctuations in estimated contact/quarantine rates, and a feedback loop between the strengthening/relaxation of intervention strategies and the recurrence of the outbreaks. Moreover, the findings show that there is diversity in the shape of the temporal evolution curves of the inferred contact/quarantine rates in the considered regions, which indicates variation in the intensity of control strategies adopted in various regions. Author summary: When applying the compartment model to simulate the disease transmission dynamics, some parameters or particular functions are assumed to describe the intensity of the control interventions. However, these preset specific functions may not accurately quantify the intervention strategies, which brings great challenges to accurately make prediction and evaluation. In this study, we developed an extended transmission-dynamics-informed neural network algorithm by integrating deep neural network with epidemic model. Even for insufficient case data, the proposed algorithm can still help us reconstruct the temporal evolution trend of the epidemic and infer unknown parameters. We inferred the time series on contract rate and quarantine rate for six regions based on the case data, on which the reasonable and interpretable functions, describing the dynamic variation in the intensity of control strategies, can be successfully selected and determined. The inferred contact/quarantine rates in various regions show the diverse shapes and regional dependent, and hence the variation in the intensity of control measures. This suggests the dynamic zero-case policy exhibits the different efficacy in reducing contacts and increasing the quarantine and isolation. [ABSTRACT FROM AUTHOR]

This paper deals with the control of a prey species (as an unwanted species) in a predator-prey system. We consider a scenario where there are two control means available and they are applied in a state-dependent impulsive way, meaning that when the population of the harmful species is lower than a preset threshold, no control measure will be implemented; while when it reaches the threshold, the two control means will be used either in alternating order or random order. We formulate a general mathematical model for this scenario to evaluate the effect of such a control strategy by exploring the dynamics of this model. We define a one-dimensional map (Poincaré map) and by using the properties of this map, we derive sufficient conditions for the existence and global stability of an order-k periodic solution. By using the analogue of Poincaré criterion and bifurcation theory, we also establish sufficient conditions for a transcritical bifurcation near the predator-free periodic solution. Finally, we apply the results for the general model to two particular cases from two distinct fields: (I) integrated pest control and (II) tumour control with a comprehensive therapy. For (I), theoretical and numerical results show that the outbreak period of the pest is longer when two pesticides are applied randomly than when the alternating strategy is used. For (II), we find that the treatment frequency of drug rotation strategy is lower than that of no drug change strategy, and that the higher the control intensity, the lower the treatment frequency. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Filippov switching model which is composed of the Lorenz and Chen systems. By employing the qualitative analysis techniques of nonsmooth dynamical systems, we show that the new Filippov system not only inherits the properties of the Lorenz and Chen systems but also presents new dynamics including new chaotic attractors such as four-wing butterfly attractor, Lorenz attractor with sliding segments, etc. In particular, we find that different new attractors can coexist such as the coexistence of two-point attractors and chaotic attractor, the coexistence of two-point attractors and quasi-periodic solution, the coexistence of transient transition chaos and quasi-periodic solution. Furthermore, nonsmooth bifurcations and numerical analyses reveal that the proposed Filippov system has a series of new sliding bifurcations including a symmetric pair of sliding mode bifurcations, a symmetric pair of sliding Hopf bifurcations, and a symmetric pair of Hopf-like boundary equilibrium bifurcations. [ABSTRACT FROM AUTHOR]

Roguing and replanting are the most common strategies to control plant diseases and pests. How to build the mathematical models of plant virus transmission and consider the impact of roguing and replanting strategies on plant virus eradication is of great practical significance. In the present paper, we propose the mathematical models for plant virus transmission with continuous and impulsive roguing control. For the model with continuous control strategies, the threshold values for the existences and stabilities of multiple equilibria have been given, and the effect of roguing strategies on the threshold values is also addressed. Furthermore, the model with impulsive roguing control tactics is proposed, and the existence and stability of the plant-only and disease-free periodic solutions of the model are investigated by calculating several threshold values. Moreover, when selecting the design control strategy to minimize the threshold, we systematically analyze the existence of the optimal times of roguing infected plants within a replanting cycle, which is of great significance to the design and optimization of the prevention and control strategy of plant virus transmission. Finally, numerical investigations are given to reveal the main conclusions, and the biological implications of the main results are briefly discussed in the last section. [ABSTRACT FROM AUTHOR]

By assuming a periodic variation in the intrinsic growth rate of the prey, a nonlinear ecological system with periodic forcing and state-dependent feedback control is proposed. The main purpose of the present paper is to study the dynamical behavior generated by periodic forcing and nonlinear impulse perturbations and their effects on pest control. To do this, we first investigate the existence and stability of the boundary periodic solution, and then we employ the numerical bifurcation techniques, mainly including one-dimensional and two-dimensional parameter bifurcation analyses, to reveal that the system exhibits rich and complex dynamic behaviors. Especially, period-adding bifurcation with chaos is found in the two-parameter bifurcation plane. Moreover, we find the periodic structure similar to Arnold tongues, and they are arranged according to the sequence of a Farey tree. In addition, one-dimensional bifurcation diagrams reveal the existence of order- k periodic, and chaotic solutions, multiple coexisting attractors, period-doubling bifurcations, period-halving bifurcations, and so on. Finally, the effects of the initial population density of pests and natural enemies on the pulse frequency and the biological significance related to the numerical results are studied and discussed. [ABSTRACT FROM AUTHOR]

During the outbreak of emerging infectious diseases, a complex interplay of random events, media messages and human emotions inevitably affects disease transmission. In this paper, we propose a new stochastic epidemic model incorporating emotional influence under three-tier media alerts. Itô’s formula, Lyapunov function method and ergodicity of Markov chain are employed to research the extinction–persistence behavior of diseases. Our findings show that early detection and reporting contribute to effective prevention. However, the intensity of reporting rates and warning thresholds will need to be chosen according to the characteristic of each epidemic. Otherwise, media coverage may have a negative impact on the human psychology of disease prevention and control. A biological paradox emerges: high reporting rate and premature activation of the third-tier media warning may increase the number of infected individuals. [ABSTRACT FROM AUTHOR]

• The various optimal control problems of a coupled SIS model for respiratory disease with air pollution are proposed. • The optimal control solutions for the deterministic and stochastic models are theoretically analyzed respectively. • Data fitting results identify unknown parameters of the models and reveal the effect of actual control measures. • The cost values for different combinations of control measures reveal air pollution reduction is the most effective. Respiratory diseases caused by inhalation of air pollutants are affected by seasonal changes and mitigated by air pollution control, resulting in complex dynamics. In order to investigate the effects of various factors such as random noise and air pollution control on respiratory diseases, we developed deterministic and stochastic two-dimensional coupled SIS models with multiple control measures. The proposed models and parameter estimation methods, including determinations of unknown parameter values, were used to fit the Air Quality Index (AQI) data for Xi'an city in recent 10 years. The existence of the optimal solutions for the deterministic and stochastic models were analyzed theoretically and provided to compare the parameter fitting solutions with the optimal solutions, and give theoretical support for seeking a more reasonable air pollution optimization prevention and control scheme. To show this, we conducted numerical simulations of the optimal control solution and state evolution trajectories under different weight coefficient ratios and control objectives. The results show that the stochastic optimal control problem is more consistent with the practical scenario. We also formulate the optimal control problem assuming that the control variable depends on the concentration of air pollutants. The optimal control solution reflected the periodic variation of the air pollution control strategy well. A comparison of cost values for different combinations of the three control measures illustrated that air pollution reduction is the most effective control measure. [ABSTRACT FROM AUTHOR]

Air pollution increases the risk of getting respiratory diseases. Both the removal of air pollutants and the transmission of diseases can be influenced by random perturbations. In this work, we develop a stochastic differential equation (SDE) model, coupled with seasonal air pollution, to study the dynamics of infectious respiratory disease spread. The periodicity of disease outbreaks is assumed to be caused by seasonal air pollution. The SDE of the air quality index (AQI) is proved to be ultimately bounded. The complexity of the SDE of infected individuals lies in the transmission rate that depends on air pollution. We prove that the system driven by the periodic clearance rate has at least one stochastic periodic solution under certain conditions. By computing the closed form of the Hermite expansion of transformation density, we construct an approximate likelihood function to fit the data of AQI and influenza-like illness cases, as a case study. Data fitting shows that the stochastic periodic model can well capture the dynamical behavior of air pollution and outbreaks of the infectious respiratory disease. We also study the impact of parameters on the reduction of air pollution and disease spread. This work shows the correlation between air pollution and infectious respiratory disease outbreaks and illustrates that the intensity of the environmental disturbance is a factor that cannot be ignored. [ABSTRACT FROM AUTHOR]

A nonlinear discrete switching host-parasitoid model with Holling type II functional response function, in which the switch is guided by an economic threshold (ET), is proposed. Thus, if the weighted density of two generations of the host population increases and exceeds the ET, then integrated pest management (IPM) measures are enacted, i.e., biological and chemical measures are implemented together, assuming that the chemical immediately precedes the biological inputs to avoid pesticide-induced deaths of the natural enemies. First, the existence and local stability of the equilibria of two subsystems were studied, and the existence and coexistence of several types of equilibria of a nonlinear switching system were analysed. Next, the nonlinear switching system was investigated by numerical simulation, showing that the system exhibits quite complex dynamic behaviour. A two-dimensional bifurcation diagram revealed the existence and coexistence regions of different types of equilibria including regular and virtual equilibria. Moreover, period-adding bifurcations in two-dimensional parameter spaces were found. One-dimensional bifurcation diagrams revealed that the system has periodic, quasiperiodic, and chaotic solutions, Neimark–Sacker bifurcation, multiple coexisting attractors, period-doubling bifurcations, period-halving bifurcations, and so on. Finally, the initial densities of hosts and parasitoids associated with host outbreaks and their biological implications are discussed. [ABSTRACT FROM AUTHOR]

The idea of action threshold depends on the pest density and its change rate is more general and furthermore can produce new modelling techniques related to integrated pest management (IPM) as compared with those that appeared in earlier studies, which definitely bring challenges to analytical analysis and generate new ideas to the state control measures. Keeping this in mind, using the strategies of IPM, we develop a prey-predator system with action threshold depending on the pest density and its change rate, and study its dynamical behavior. We develop new criteria guaranteeing the existence, uniqueness, local and global stability of order-1 periodic solutions. Applying the properties of Lambert W function, the Poincaré map is portrayed for the exact phase set, which is helpful to provide the sufficient conditions for the existence and stability of the interior order-1 periodic solutions and boundary order-1 periodic solution, also confirmed by numerical simulations. It is studied in detail that how and under what conditions the fixed point of Poincaré map and its stability are affected by the newly introduced action threshold. The analytical methods developed in this paper will be very beneficial to study other generalized models with state-dependent feedback control. [ABSTRACT FROM AUTHOR]

The development of pesticide resistance significantly affects the outcomes of pest control. A quantitative depiction of the effects of pesticide resistance development on integrated pest management (IPM) strategies and pest control outcomes is challenging. To address this problem, a discrete host-parasitoid model with pesticide resistance development and IPM strategies is proposed and analyzed. The threshold condition of pest eradication which reveals the relationship between the development of pest resistance and the rate of natural enemy releases is provided and analyzed, and the optimal rate for releasing natural enemies was obtained based on this threshold condition. Furthermore, in order to reduce adverse effects of the pesticide on natural enemies, the model has been extended to consider the spraying of pesticide and releases of natural enemies at different times. The effects of the dynamic complexity and different resistance development equations on the main results are also discussed. [ABSTRACT FROM AUTHOR]

The impact of air pollution on people’s health and daily activities in China has recently aroused much attention. By using stochastic differential equations, variation in a 6 year long time series of air quality index (AQI) data, gathered from air quality monitoring sites in Xi’an from 15 November 2010 to 14 November 2016 was studied. Every year the extent of air pollution shifts from being serious to not so serious due to alterations in heat production systems. The distribution of such changes can be predicted by a Bayesian approach and the Gibbs sampler algorithm. The intervals between changes in a sequence indicate when the air pollution becomes increasingly serious. Also, the inflow rate of pollutants during the main pollution periods each year has an increasing trend. This study used a stochastic SEIS model associated with the AQI to explore the impact of air pollution on respiratory infections. Good fits to both the AQI data and the numbers of influenza-like illness cases were obtained by stochastic numerical simulation of the model. Based on the model’s dynamics, the AQI time series and the daily number of respiratory infection cases under various government intervention measures and human protection strategies were forecasted. The AQI data in the last 15 months verified that government interventions on vehicles are effective in controlling air pollution, thus providing numerical support for policy formulation to address the haze crisis. [ABSTRACT FROM AUTHOR]

A planar predator–prey impacting system model with a nonmonotonic functional response function is proposed and analyzed. The existence and stability of a boundary order-1 periodic solution were investigated and the threshold conditions for a transcritical bifurcation and stable switching were obtained, and also the definition and properties of the Poincaré map are discussed. The main results indicate that multiple discontinuous points of the Poincaré map could induce the coexistence of multiple order-1 periodic solutions. Numerical analyses reveal the complex dynamics of the model including periodic adding and halving bifurcations, which could result in multiple active phases, among them rapid spiking and quiescence phases which can switch from one to another and consequently create complex bursting patterns. The main results reveal that it is beneficial to restore the stability and balance of a ecosystem for species with group defence by moderately reducing population densities and the group defence capacity. [ABSTRACT FROM AUTHOR]

The present study considers the robust stability for impulsive complex-valued neural networks (CVNNs) with discrete time delays. By applying the homeomorphic mapping theorem and some inequalities in a complex domain, some sufficient conditions are obtained to prove the existence and uniqueness of the equilibrium for the CVNNs. By constructing appropriate Lyapunov-Krasovskii functionals and employing the complex-valued matrix inequality skills, the study finds the conditions to guarantee its global robust stability. A numerical simulation illustrates the correctness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states. Numerical simulations have been performed to illustrate the theoretical results and evaluate the effects of time delays and fractions of infection leading to latency on the virus dynamics. The estimates of the relative contributions to the HIV latent reservoir and the virus population from the two modes of transmission have also been provided. [ABSTRACT FROM PUBLISHER]

In order to comprehend the effects of the duration of pesticide residual effectiveness on successful pest control, a stochastic integrated pest management (IPM) model with pesticides which have residual effects is proposed. Firstly, we show that our model has a global and positive solution and give its explicit expression when pest goes extinct. Then the sufficient conditions for pest extinction combined with the ones for the global attractivity of the pest solution only chemical control are established. Moreover, we also derive sufficient conditions for weak persistence which show that the solution of stochastic IPM models is stochastically ultimately bounded under some conditions. [ABSTRACT FROM AUTHOR]

An outbreak of dengue fever in Guangdong province in 2014 was the most serious outbreak ever recorded in China. Given the known positive correlation between the abundance of mosquitoes and the number of dengue fever cases, a stage structured mosquito model was developed to investigate the cause of the large abundance of mosquitoes in 2014 and its implications for outbreaks of the disease. Data on the Breteau index (number of containers positive for larvae per 100 premises investigated), temperature and precipitation were used for model fitting. The egg laying rate, the development rate and the mortality rates of immatures and adults were obtained from the estimated parameters. Moreover, effects of daily fluctuations of temperature on these parameters were obtained and the effects of temperature and precipitation were analyzed by simulations. Our results indicated that the abundance of mosquitoes depended not only on the total annual precipitation but also on the distribution of the precipitation. The daily mean temperature had a nonlinear relationship with the abundance of mosquitoes, and large diurnal temperature differences can reduce the abundance of mosquitoes. In addition, effects of increasing precipitation and temperature were interdependent. Our findings suggest that the large abundance of mosquitoes in 2014 was mainly caused by the distribution of the precipitation. In the perspective of mosquito control, our results reveal that it is better to clear water early and spray insecticide between April and August in case of limited resources. [ABSTRACT FROM AUTHOR]

Insects such as locusts and some moths can transform from a solitarious phase when they remain in loose populations and a gregarious phase, when they may swarm. Therefore, the key to effective management of outbreaks of species such as the desert locust Schistocercagregaria is early detection of when they are in the threshold state between the two phases, followed by timely control of their hopper stages before they fledge because the control of flying adult swarms is costly and often ineffective. Definitions of gregarization thresholds should assist preventive control measures and avoid treatment of areas that might not lead to gregarization. In order to better understand the effects of the threshold density which represents the gregarization threshold on the outbreak of a locust population, we developed a model of a discrete switching system. The proposed model allows us to address: (1) How frequently switching occurs from solitarious to gregarious phases and vice versa; (2) When do stable switching transients occur, the existence of which indicate that solutions with larger amplitudes can switch to a stable attractor with a value less than the switching threshold density?; and (3) How does random perturbation influence the switching pattern? Our results show that both subsystems have refuge equilibrium points, outbreak equilibrium points and bistable equilibria. Further, the outbreak equilibrium points and bistable equilibria can coexist for a wide range of parameters and can switch from one to another. This type of switching is sensitive to the intrinsic growth rate and the initial values of the locust population, and may result in locust population outbreaks and phase switching once a small perturbation occurs. Moreover, the simulation results indicate that the switching transient patterns become identical after some generations, suggesting that the evolving process of the perturbation system is not related to the initial value after some fixed number of generations for the same stochastic processes. However, the switching frequency and outbreak patterns can be significantly affected by the intensity of noise and the intrinsic growth rate of the locust population. [ABSTRACT FROM AUTHOR]

Dengue fever has rapidly become the world's most common vector-borne viral disease. Use of endosymbiotic Wolbachia is an innovative technology to prevent vector mosquitoes from reproducing and so break the cycle of dengue transmission. However, strategies such as population eradication and replacement will only succeed if appropriate augmentations with Wolbachia-infected mosquitoes that take account of a variety of factors are carried out. Here, we describe the spread of Wolbachia in mosquito populations using an impulsive differential system with four state variables, incorporating the effects of cytoplasmic incompatibility and the augmentation of Wolbachia-infected mosquitoes with different sex ratios. We then evaluated (a) how each parameter value contributes to the success of population replacement; (b) how different release quantities of infected mosquitoes with different sex ratios affect the success of population suppression or replacement; and (c) how the success of these two strategies can be realized to block the transmission of dengue fever. Analysis of the system's stability, bifurcations and sensitivity reveals the existence of forward and backward bifurcations, multiple attractors and the contribution of each parameter to the success of the strategies. The results indicate that the initial density of mosquitoes, the quantities of mosquitoes released in augmentations and their sex ratios have impacts on whether or not the strategies of population suppression or replacement can be achieved. Therefore, successful strategies rely on selecting suitable strains of Wolbachia and carefully designing the mosquito augmentation program. [ABSTRACT FROM AUTHOR]

In reality, the outbreak of emerging infectious diseases including SARS, A/H1N1 and Ebola are accompanied by the common cold and flu. The selective treatment measure for mitigating and controlling the emerging infectious diseases should be implemented due to limited medical resources. However, how to determine the threshold infected cases and when to implement the selective treatment tactics are crucial for disease control. To address this, we derive a non-smooth Filippov system induced by selective treatment measure. The dynamic behaviors of two subsystems have been discussed completely, and the existence conditions for sliding segment, sliding mode dynamics and different types of equilibria such as regular equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point have been provided. Further, numerical sliding bifurcation analyses show that the proposed Filippov system has rich sliding bifurcations. Especially, the most interesting results are those for the fixed parameter set as the bifurcation parameter varies, the sliding bifurcations occur sequentially: crossing → buckling → real/virtual equilibrium → buckling → crossing. The key factors which affect the selective treatment measures and the threshold value of infected cases for emerging infectious disease have been discussed in more detail. [ABSTRACT FROM AUTHOR]

With the evolution of pest resistance to Bt-corn, farmers’ economic losses are increasing. However, a planting strategy with Bt-corn mixed with non-Bt-corn to fight the development of pest resistance can be efficient. Nevertheless, this mixed strategy poses questions such as (1) what is the optimal ratio of Bt-corn to non-Bt-corn that should be planted in a field? And (2) what is the main factor affecting the farmers’ net present value? To address these questions, we propose and investigate a discrete pest growth model with pest resistance to Bt-corn. According to the model’s economic functions, the main factors affecting the farmers’ net present value are presented and discussed. By comparing the net present values of a pure Bt-corn planting strategy with the mixed planting strategy, an optimal planting strategy was devised. Moreover, the optimal ratio of Bt-corn to non-Bt-corn to be planted when the mixed planting strategy is implemented in the field was also investigated. [ABSTRACT FROM AUTHOR]

News reporting has the potential to modify a community׳s knowledge of emerging infectious diseases and affect peoples’ attitudes and behavior. Here we developed a quantitative approach to evaluate the effects of media on such behavior. Statistically significant correlations between the number of new hospital notifications, during the 2009 A/H1N1 influenza epidemic in the Shaanxi province of China, and the number of daily news items added to eight major websites were found from Pearson correlation and cross-correlation analyses. We also proposed a novel model to examine the implication for transmission dynamics of these correlations. The model incorporated the media impact function into the intensity of infection, and enhanced the traditional epidemic SEIR model with the addition of media dynamics. We used a nonlinear least squares estimation to identify the best-fit parameter values in the model from the observed data. We also carried out the uncertainty and sensitivity analyses to determine key parameters during early phase of the disease outbreak for the final outcome of the outbreak with media impact. The findings confirm the importance of responses by individuals to the media reports, with behavior changes having important consequence for the emerging infectious disease control. Therefore, for mitigating emerging infectious diseases, media reports should be focused on how to guide people׳s behavioral changes, which are critical for limiting the spread of disease. [ABSTRACT FROM AUTHOR]

We propose a Holling II predator–prey model with nonlinear pulse as state-dependent feedback control strategy and then provide a comprehensively qualitative analysis by using the theories of impulsive semi-dynamical systems. First, the Poincaré map is constructed based on the domains of impulsive and phase sets which are defined according to the phase portraits of the model. Second, the threshold conditions for the existence and stability of the semi-trivial periodic solution are given, and subsequently an order-1 periodic solution is generated through the transcritical bifurcation. Furthermore, the different parameter spaces for the existence and stability of an order-1 periodic solution are investigated. In addition, the existence and nonexistence of order- k ( k ≥ 2 ) periodic solutions have been studied theoretically. Moreover, the numerical investigations are presented in order to substantiate our theoretical results and show the complex dynamics of proposed model. Finally, some biological implications of the mathematical results are discussed in the conclusion section. [ABSTRACT FROM AUTHOR]

In the present paper, we perform a complete bifurcation analysis of a two-stage population model, in which the per capita birth rate and stage transition rate from juveniles to adults are density dependent and take the general Beverton-Holt functions. Our study reveals a rich bifurcation structure including codimension-one bifurcations such as saddle-node, Hopf, homoclinic bifurcations, and codimension-two bifurcations such as Bogdanov-Takens (BT), Bautin bifurcations, etc. Moreover, by employing the polynomial analysis and approximation techniques, the existences of equilibria, Hopf and BT bifurcations as well as the formulas for calculating their bifurcation sets have been provided. Finally, the complete bifurcation diagrams and associate phase portraits are obtained not only analytically but also confirmed and extended numerically. [ABSTRACT FROM AUTHOR]

The main purpose is to develop novel analytical techniques and provide a comprehensive qualitative analysis of global dynamics for a state-dependent feedback control system arising from biological applications including integrated pest management. The model considered consists of a planar system of differential equations with state-dependent impulsive control. We characterize the impulsive and phase sets, using the phase portraits of the planar system and the Lambert W function to define the Poincaré map for impulsive point series defined in the phase set. The existence, local and global stability of an order-1 limit cycle and obtain sharp sufficient conditions for the global stability of the boundary order-1 limit cycle have been provided. We further examine the flip bifurcation related to the existence of an order-2 limit cycle. We show that the existence of an order-2 limit cycle implies the existence of an order-1 limit cycle. We derive sufficient conditions under which any trajectory initiating from a phase set will be free from impulsive effects after finite state-dependent feedback control actions, and we also prove that order- k ( $k\geq3$) limit cycles do not exist, providing a solution to an open problem in the integrated pest management community. We then investigate multiple attractors and their basins of attraction, as well as the interior structure of a horseshoe-like attractor. We also discuss implications of the global dynamics for integrated pest management strategy. The analytical techniques and qualitative methods developed in the present paper could be widely used in many fields concerning state-dependent feedback control. [ABSTRACT FROM AUTHOR]

How to use chemical and biological control in sensible combinations has been a concern of many agriculture departments and ecologists. To address this problem, a pest-natural enemy model with disease in the pest and with different frequencies of pesticide sprays and of releases of both infected pests and natural enemies is proposed and analyzed by using impulsive differential equations. The threshold conditions for susceptible pest (or total pest) eradication periodic solution are provided for different scenarios. In particular, two different natural enemy release strategies and two different pest control tactics are investigated and compared in detail. Furthermore, the effects of the frequency of pesticide applications and the frequency of natural enemy and infected pest releases on the threshold values are discussed. The results indicate that there exists an optimal frequency of pesticide application or an optimal releasing period which minimizes the threshold value. This information may help pest control experts to decide on the optimum timing for spray applications and optimum rates for releases. [ABSTRACT FROM AUTHOR]

The aim of the present study is to apply simple ODE models in the area of modeling the spread of emerging infectious diseases and show the importance of model selection in estimating parameters, the basic reproduction number, turning point, and final size. To quantify the plausibility of each model, given the data and the set of four models including Logistic, Gompertz, Rosenzweg, and Richards models, the Bayes factors are calculated and the precise estimates of the best fitted model parameters and key epidemic characteristics have been obtained. In particular, for Ebola the basic reproduction numbers are 1.3522 (95% CI (1.3506, 1.3537)), 1.2101 (95% CI (1.2084, 1.2119)), 3.0234 (95% CI (2.6063, 3.4881)), and 1.9018 (95% CI (1.8565, 1.9478)), the turning points are November 7,November 17, October 2, and November 3, 2014, and the final sizes until December 2015 are 25794 (95% CI (25630, 25958)), 3916 (95% CI (3865, 3967)), 9886 (95% CI (9740, 10031)), and 12633 (95% CI (12515, 12750)) for West Africa, Guinea, Liberia, and Sierra Leone, respectively. The main results confirm that model selection is crucial in evaluating and predicting the important quantities describing the emerging infectious diseases, and arbitrarily picking a model without any consideration of alternatives is problematic. [ABSTRACT FROM AUTHOR]

A Filippov crop-pest-natural enemy ecological system with threshold switching surface related to the pest control is developed, which has been completely analyzed by employing the qualitative techniques of non-smooth dynamical systems. The main results reveal that the proposed switching model can have multiple pseudo-equilibria in the sliding region, which result in rich bifurcations in the sliding region including saddle-node, Hopf, Bogdanov-Takens and Hopf-like boundary equilibrium bifurcations. Moreover, the pseudo-periodic solution (or pseudo-homoclinic loop) can be generated in the sliding region through a Hopf bifurcation (or a homoclinic bifurcation), which can collide with the tangential lines at the cusp singularities and finally disappears as parameter varies. This reveals that although the system can stabilize on the sliding region to achieve the purpose of pest control, there are complex dynamical behaviors and sliding bifurcations within the sliding region. Furthermore, as the threshold level varies, the model exhibits the interesting global sliding bifurcations including grazing bifurcation, buckling bifurcation, crossing bifurcation, homoclinic bifurcation to a pseudo-saddle, period-halving bifurcation and chaotic dynamics. This implies that control outcomes are sensitive to the threshold level, and hence it is crucial to choose the threshold level to initiate control strategy. [ABSTRACT FROM AUTHOR]

Fragmented habitat patches between which plants and animals can disperse can be modeled as networks with varying degrees of connectivity. A predator-prey model with network structures is proposed for integrated pest management (IPM) with impulsive control actions. The model was analyzed using numerical methods to investigate how factors such as the impulsive period, the releasing constant of natural enemies and the mode of connections between the patches affect pest outbreak patterns and the success or failure of pest control. The concept of the cluster as defined by Holland and Hastings is used to describe variations in results ranging from global synchrony when all patches have identical fluctuations to n-cluster solutions with all patches having different dynamics. Heterogeneity in the initial densities of either pest or natural enemy generally resulted in a variety of cluster oscillations. Surprisingly, if n > 1, the clusters fall into two groups one with low amplitude fluctuations and the other with high amplitude fluctuations (i.e. duality in phase space), implying that control actions radically alter the system's characteristics by inducing duality and more complex dynamics. When the impulsive period is small enough, i.e. the control strategy is undertaken frequently, the pest can be eradicated. As the period increases, the pest's dynamics shift from a steady state to become chaotic with periodic windows and more multicluster oscillations arise for heterogenous initial density distributions. Period-doubling bifurcation and periodic halving cascades occur as the releasing constant of the natural enemy increases. For the same ecological system with five differently connected networks, as the randomness of the connectedness increases, the transient duration becomes smaller and the probability of multicluster oscillations appearing becomes higher. [ABSTRACT FROM AUTHOR]

Combining biological and chemical control has been an efficient strategy to combat the evolution of pesticide resistance. Continuous releases of natural enemies could reduce the impact of a pesticide on them and the number to be released should be adapted to the development of pesticide resistance. To provide some insights towards this adaptation strategy, we developed a novel pest–natural enemy model considering both resistance development and inoculative releases of natural enemies. Three releasing functions which ensure the extinction of the pest population are proposed and their corresponding threshold conditions obtained. Aiming to eradicate the pest population, an analytic formula for the number of natural enemies to be released was obtained for each of the three different releasing functions, with emphasis on their biological implications. The results can assist in the design of appropriate control strategies and decision-making in pest management. [ABSTRACT FROM AUTHOR]

Locusts and some noctuid moths exhibit polyphenism whereby they can change their “phase” from a solitary (“solitarious”) condition to a gregarious one. Gregarious phase insects are often migratory travelling from recession areas into larger invasion zones and, among locusts, occur in swarms. Difference equation models of the population dynamics of insects that take account of such changes between solitarious or gregarious phases in relation to predation, both with and without time delays, are described. Solutions of the models are non-linear. Chaotic solutions are obtainable under some circumstances even with very low values for the intrinsic rate of increase in the prey population, in contrast to previous conclusions from models without predation. Comparisons with the results obtained for single species with those obtained in this paper show that predation can reduce (i) the average density of the prey, (ii) durations of periods when the populations stay in the gregarious phase, and (iii) the frequency of their shifts from the solitarious state to the gregarious form. Similar results are obtained if a time delay is introduced to mimic a transient phase. With a wide range of parameter values, models including predation with or without random perturbation reveal several stable attractors for phase diagrams of the populations, which are biologically meaningful compared with empirical datasets and which were unobtainable without predation, suggesting that inclusion of predation and time delays improved the realism of the models. However, comparisons between autocorrelation analyses of locust time-series, but of swarms only, with those of model outputs suggest that inclusion of the time delay leads to less, not more, realism. The prediction of non-linearity in the dynamics of migrant insects with phase changes and its significance for forecasting to aid control is briefly discussed in relation to published data on the desert locust Schistocerca gregaria. [ABSTRACT FROM AUTHOR]

A Filippov system is proposed to describe the stage structured nonsmooth pest growth with threshold policy control (TPC). The TPC measure is represented by the total density of both juveniles and adults being chosen as an index for decisions on when to implement chemical control strategies. The proposed Filippov system can have three pieces of sliding segments and three pseudo-equilibria, which result in rich sliding mode bifurcations and local sliding bifurcations including boundary node (boundary focus, or boundary saddle) and tangency bifurcations. As the threshold density varies the model exhibits the interesting global sliding bifurcations sequentially: touching → buckling → crossing → sliding homoclinic orbit to a pseudo-saddle → crossing → touching bifurcations. In particular, bifurcation of a homoclinic orbit to a pseudo-saddle with a figure of eight shape, to a pseudo-saddle-node or to a standard saddle-node have been observed for some parameter sets. This implies that control outcomes are sensitive to the threshold level, and hence it is crucial to choose the threshold level to initiate control strategy. One more sliding segment (or pseudo-equilibrium) is induced by the total density of a population guided switching policy, compared to only the juvenile density guided policy, implying that this control policy is more effective in terms of preventing multiple pest outbreaks or causing the density of pests to stabilize at a desired level such as an economic threshold. [ABSTRACT FROM AUTHOR]

Background: Epidemic zoning is an important option in a series of measures for the prevention and control of infectious diseases. We aim to accurately assess the disease transmission process by considering the epidemic zoning, and we take two epidemics with distinct outbreak sizes as an example, i.e., the Xi'an epidemic in late 2021 and the Shanghai epidemic in early 2022. Methods: For the two epidemics, the total cases were clearly distinguished by their reporting zone and the Bernoulli counting process was used to describe whether one infected case in society would be reported in control zones or not. Assuming the imperfect or perfect isolation policy in control zones, the transmission processes are respectively simulated by the adjusted renewal equation with case importation, which can be derived on the basis of the Bellman-Harris branching theory. The likelihood function containing unknown parameters is then constructed by assuming the daily number of new cases reported in control zones follows a Poisson distribution. All the unknown parameters were obtained by the maximum likelihood estimation. Results: For both epidemics, the internal infections characterized by subcritical transmission within the control zones were verified, and the median control reproduction numbers were estimated as 0.403 (95% confidence interval (CI): 0.352, 0.459) in Xi'an epidemic and 0.727 (95% CI: 0.724, 0.730) in Shanghai epidemic, respectively. In addition, although the detection rate of social cases quickly increased to 100% during the decline period of daily new cases until the end of the epidemic, the detection rate in Xi'an was significantly higher than that in Shanghai in the previous period. Conclusions: The comparative analysis of the two epidemics with different consequences highlights the role of the higher detection rate of social cases since the beginning of the epidemic and the reduced transmission risk in control zones throughout the outbreak. Strengthening the detection of social infection and strictly implementing the isolation policy are of great significance to avoid a larger-scale epidemic. [ABSTRACT FROM AUTHOR]

Although single factors such as rainfall are known to affect the population dynamics of Aedes albopictus, the main vector of dengue fever in Eurasia, the synergistic effects of different meteorological factors are not fully understood. To address this topic, we used meteorological data and mosquito-vector association data including Breteau and ovitrap indices in key areas of dengue outbreaks in Guangdong Province, China, to formulate a five-stage mathematical model for Aedes albopictus population dynamics by integrating multiple meteorological factors. Unknown parameters were estimated using a genetic algorithm, and the results were analyzed by k-Shape clustering, random forest and grey correlation analysis. In addition, the population density of mosquitoes in 2022 was predicted and used for evaluating the effectiveness of the model. We found that there is spatiotemporal heterogeneity in the effects of temperature and rainfall and their distribution characteristics on the diapause period, the numbers of peaks in mosquito densities in summer and the annual total numbers of adult mosquitoes. Moreover, we identified the key meteorological indicators of the mosquito quantity at each stage and that rainfall (seasonal rainfall and annual total rainfall) was more important than the temperature distribution (seasonal average temperature and temperature index) and the uniformity of rainfall annual distribution (coefficient of variation) for most of the areas studied. The peak rainfall during the summer is the best indicator of mosquito population development. The results provide important theoretical support for the future design of mosquito vector control strategies and early warnings of mosquito-borne diseases. Author summary: The study and control of the numbers of Aedes albopictus, the main vector of dengue fever in China, is crucial for the prevention and control of this mosquito-borne disease. Due to the major impact of rainfall and temperature on mosquito population sizes, we built a mathematical model based on the life cycle of mosquitoes and meteorological and mosquito vector monitoring data in Guangdong Province. Through this model, we explored the effects of temperature, rainfall and their distribution characteristics on the development of the mosquito population and found that they had different effects on the developing stages of mosquitoes in different periods and different locations. Moreover, according to the established meteorological indicators and their importance ranking, it was found that for most areas of Guangdong Province, rainfall was more important than the temperature distribution and the evenness of rainfall distribution, and that the peak rainfall in summer was the best predictor of mosquito population development. In addition, we also developed a method to utilize previous experience in mosquito control, which together with the above conclusions will be of great help in the design of future mosquito vector control strategies and the prediction and early warning of mosquito-borne diseases. [ABSTRACT FROM AUTHOR]

Past seasonal influenza epidemics and vaccination experience may affect individuals' decisions on whether to be vaccinated or not, decisions that may be constantly reassessed in relation to recent influenza related experience. To understand the potentially complex interaction between experience and decisions and whether the vaccination rate is likely to reach a critical coverage level or not, we construct an adaptive‐decision model. This model is then coupled with an influenza vaccination dynamics (SIRV) model to explore the interaction between individuals' decision‐making and an influenza epidemic. Nonlinear least squares estimation is used to obtain the best‐fit parameter values in the SIRV model based on data on new influenza‐like illness (ILI) cases in Texas. Uncertainty and sensitivity analyses are then carried out to determine the impact of key parameters of the adaptive decision‐making model on the ILI epidemic. The results showed that the necessary critical coverage rate of ILI vaccination could not be reached by voluntary vaccination. However, it could be reached in the fourth year if mass media reports improved individuals' memory of past vaccination experience. Individuals' memory of past vaccination experience, the proportion with histories of past vaccinations and the perceived cost of vaccination are important factors determining whether an ILI epidemic can be effectively controlled or not. Therefore, health authorities should guide people to improve their memory of past vaccination experience through media reports, publish timely data on annual vaccination proportions and adjust relevant measures to appropriately reduce vaccination perceived cost, in order to effectively control an ILI epidemic. [ABSTRACT FROM AUTHOR]

Abstract: In a prey–predator model, an effective management strategy called the threshold policy control (TPC) is proposed, resulting in Filippov system. Considering the limitation of environmental resources, Filippov system with the weighted sum as the index is put forward in the prey–predator model with Ivlev’s function response. Firstly, the existences of sliding segments in four cases have been discussed completely. Further, the sliding mode dynamics, the existences of different types of equilibria and tangent point, regular/virtual equilibrium and sliding mode bifurcations have been addressed. Moreover, the results obtained in present work indicate that the local sliding bifurcations such as boundary focus, boundary node and tangent bifurcations occur sequentially with the threshold value varying. Finally, some global sliding bifurcations including touching and buckling bifurcations are investigated by employing numerical techniques. [Copyright &y& Elsevier]

Integrated pest management options such as combining chemical and biological control are optimal for combating pesticide resistance, but pose questions if a pest is to be controlled to extinction. These questions include (i) what is the relationship between the evolution of pesticide resistance and the number of natural enemies released? (ii) How does the cumulative number of natural enemies dying affect the number of natural enemies to be released? To address these questions, we developed two novel pest-natural enemy interaction models incorporating the evolution of pesticide resistance. We investigated the number of natural enemies to be released when threshold conditions for the extinction of the pest population in two different control tactics are reached. Our results show that the number of natural enemies to be released to ensure pest eradication in the presence of increasing pesticide resistance can be determined analytically and depends on the cumulative number of dead natural enemies before the next scheduled release time. [ABSTRACT FROM AUTHOR]

Abstract: A non-smooth Gause predator–prey model with a constant refuge is proposed and analyzed. Firstly, the existence and stability of regular, virtual, pseudo-equilibria and tangent points are addressed. Then the relations between the existence of a regular equilibrium and a pseudo-equilibrium are studied, and the results indicate that the two types of equilibria cannot coexist. The sufficient and necessary conditions for the global stability of limit cycle, sliding touching cycle, canard cycle, focus point and pseudo-equilibrium are provided by using qualitative analysis techniques of non-smooth Filippov dynamic systems. Furthermore, sliding bifurcations related to boundary node (focus) and touching bifurcations were investigated by employing theoretical and numerical techniques. Finally, we compare our results with previous studies on a non-smooth Gause predator–prey model without involving a carrying capacity for the prey population, and some biological implications are discussed. [Copyright &y& Elsevier]