Agent-based Monte Carlo simulations for reaction–diffusion models, population dynamics, and epidemic spreading

Terrain visualization information integration in agent-based military industrial logistics simulation

The quasistationary and transient (nanosecond) regimes of nonlinear vortex dynamics in a soft magnetic dot driven by an oscillating external field are studied. We derive a nonlinear dynamical system of equations for the vortex core position and phase, assuming that the main source of nonlinearity comes from the magnetostatic energy. In the stationary regime, we demonstrate the occurrence of a fold-over bifurcation and calculate analytically the resonant nonlinear vortex frequencies as a function of the amplitude and frequency of the applied driving field. In the transient regime, we show that the vortex core dynamics are described by an oscillating trajectory radius. The resulting dynamics contain multiple frequencies with amplitude decaying in time. Finally, we evaluate the ranges of the system parameters leading to a vortex core instability (core polarization reversal).

Epidemic spreading with migration in networked metapopulation

Dynamics of epidemic spreading with vaccination: Impact of social pressure and engagement

Traffic-driven SIR epidemic spread dynamics on scale-free networks

The influence of individual emotions on the coupled model of unconfirmed information propagation and epidemic spreading in multilayer networks

Dynamics of COVID-19 spreading model with social media public health awareness diffusion over multiplex networks: Analysis and control

Due to the continuous variant of the COVID-19 virus, the present epidemic may persist in a long time, and each breakout displays strongly region/time-dependent characteristics. Prediction for each specific bursting is the basic task for the corresponding strategies. However, the refinement of the prevention and control measures implies generally the limitation of available records for the evolution of the spreading, which leads to a special difficulty for predictions. Taking into account of the interdependence of people's travel behaviors and the epidemic spreading, we proposed an Modified Logistic Model to mimic the COVID-19 epidemic spreading, to predict with limited epidemic related records the evolutionary behaviors for a specific bursting in a megacity. It reproduces successively the COVID-19 infected records in Shanghai China in the duration from March 1 to June 28,2022. Since December 7, 2022 when a new refinement of the prevention and control measures is adopted in the Mainland China, the COVID-19 epidemic blew up on a national-wide scale, and the drug "ibuprofen" is widely taken by the infected people themselves to relieve the fever symptoms. A reasonable assumption is that the total searching times for the word "ibuprofen" is a good representation for the amount of the infected people. By using the searching times for the word "ibuprofen" provided on Baidu, a famous searching platform in Mainland China, we estimated the parameters in the Modified Logistic Model and predicted subsequently the epidemic spreading behavior in Shanghai China starting from December 1, 2022. It will persist for a period of 72 days. The amount of the infected people will increase exponentially in the duration from the beginning to the 24th day, reach summit at the 31th day, and decrease exponentially in the duration from the 38th day to the end. Within the two weeks centered at the summit the increasing and decreasing speeds are both significantly small, but the increased amount of infected people each day is significantly large. The characteristics for this prediction match very well with that for the amount of metro passengers in Shanghai. As a proposal, the related departments should setup a monitoring system according to the principles of sampling in statistics, composing of some communities, hospitals, etc., to provide researchers with reliable records for prediction.

Epidemic spreading with awareness on multi-layer activity-driven networks

Quantitative agent-based firm dynamics simulation with parameters estimated by financial and transaction data analysis

Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients, but only leads to seizure freedom for roughly two in three patients. To address this problem, we designed a patient-specific epilepsy surgery model combining large-scale magnetoencephalography (MEG) brain networks with an epidemic spreading model. This simple model was enough to reproduce the stereo-tactical electroencephalography (SEEG) seizure propagation patterns of all patients (N = 15), when considering the resection areas (RA) as the epidemic seed. Moreover, the goodness of fit of the model predicted surgical outcome. Once adapted for each patient, the model can generate alternative hypothesis of the seizure onset zone and test different resection strategies in silico. Overall, our findings indicate that spreading models based on patient-specific MEG connectivity can be used to predict surgical outcomes, with better fit results and greater reduction on seizure propagation linked to higher likelihood of seizure freedom after surgery. Finally, we introduced a population model that can be individualized by considering only the patient-specific MEG network, and showed that it not only conserves but improves the group classification. Thus, it may pave the way to generalize this framework to patients without SEEG recordings, reduce the risk of overfitting and improve the stability of the analyses.

It is 10 years since Mortimer, Sutton & Gould (1989) reviewed the use of models to describe the population dynamics of weeds, and the utility of such modelling in the design of weed control programmes in annual crops. Their motivation was clearly stated: ‘A primary and strategic aim of weed ecology is to be able to explain and ultimately predict which weed species may become abundant and moreover the levels of abundance they may achieve under particular management practices.’ In the decade since this was written, have we moved closer to being able to explain and predict the population dynamics of weeds? Mortimer et al. (1989) approached weed population dynamics via ‘vertical’ studies of weed population dynamics, in which mathematical models of density-dependent responses are used to predict long-term trends in population density. Thus, as a starting point, Mortimer et al. (1989) adopted the underlying relationship to describe the future weed population Nt+1 in terms of the population in the previous generation Nt and a non-linear, density-dependent function F(Nt). Typically, F(Nt) is characterized from short-term experimentation, as there are few long-term ‘horizontal’ data sets (time series) from which information about weed population dynamics can be extracted. Simple deterministic models like equation 1 may give rise to complex (chaotic and cyclical) dynamics (May & Oster 1976). Thus, we are immediately faced with a problem. If the models we use to describe weed population dynamics can give rise to complex – possibly chaotic – dynamic behaviour, will they ever be useful in predicting levels of weed abundance at the field scale? In weed population biology, the way round this difficulty has often been to adopt a particular form of F(Nt), and estimate its parameters from experimental data – typically in the form of a graphical plot of Nt+1 against Nt. If these estimates fall clearly in the zone of parameter space for which the model dynamics are known to be non-chaotic, the dynamics of the population are regarded as non-chaotic. On the basis of this type of analysis, conducted for a large number of data sets, it may appear that the qualitative dynamics of weed populations are, essentially, such that complex dynamics will not occur in real (as opposed to model) systems. This is one way to answer the question of the utility of simple models with (possibly) complex dynamics. Thus, Cousens & Mortimer (1995) state: ‘It would therefore appear that complex behaviour such as chaos is likely to be more of a mathematical property of our models than a behaviour to be expected of real populations of annual plants.’Cousens's (1995) review of vertical studies of weed population dynamics is in emphatic agreement, noting also that incorporation of additional model parameters describing seed mortality and seed dormancy virtually rules out the possibility of oscillatory dynamics. Under the scheme of such vertical studies, an understanding of the dynamics of weed populations ‘in the real world’ depends on the characteristics of intrinsically regulatory factors and a knowledge of their interaction with various exogenous factors (Cousens & Mortimer 1995). F(Nt) describes an intrinsic regulatory signal, and the first task of the modeller is, essentially, to extract this signal from the obscuring ‘noise’. Cousens's (1995) review tells us that this is easier said than done. Population data from ‘the real world’ rarely – if ever – lie exactly on some smooth density-dependent function of N. Among the difficulties then faced (see e.g. Nisbet, Blyth & Gurney 1989; Morris 1990) are that one particular model has been chosen when different models may fit the same data equally well yet make different predictions about dynamics, and that simple models may fail to capture observed population dynamics. A recent example is provided by an elegant experimental study of the dynamics of the annual greenhouse weed Cardamine pensylvanica in controlled-environment growth chambers (Crone & Taylor 1996). The experiment produced a long (by the standards of plant population ecology) time-series data set, extending over 15 generations. All the experimental populations exhibited complex dynamics over the period of the experiment. A number of population models were fitted to the time-series data. In addition to models of the form of equation 1, models of the form were fitted. All the models explained significant amounts of variation, but only models that incorporated two-generation lagged density dependence (equation 2) reproduced the qualitative (cyclical) dynamics of the experimental populations. Models incorporating only the one-generation lag predicted stable dynamics. In further work on the same theme, Crone (1997a,b) went on to investigate the role of parental density effects (i.e. density dependence relating Nt+1 to Nt−1) in single-species populations and in interacting populations. Modelling studies indicated (as might be expected) that the inclusion of parental density effects decreased the range of parameter values for which a stable equilibrium population was the predicted outcome. Experimental studies (again with Cardamine pensylvanica) showed that, although weaker than offspring density effects (i.e. density dependence relating Nt+1 to Nt), parental density effects were large enough to change the predicted dynamics of populations. Another recent discussion of complex population dynamics has an agricultural context (Wallinga & van Oijen 1997). For their general model, Mortimer et al. (1989) adopted the widely studied form F(N) = R(1 + aN)−b, in which R is the asymptotic per capita rate of increase at low population density, and a and b are parameters describing the form and intensity of density dependence. However, in agriculture, weed populations may be controlled, and so not be left to follow dynamics depending only on their endogenous demographic parameters and Mother Nature's array of environmental effects. To model the effects of (density-independent) weed control, Mortimer et al. (1989) modified their version of equation 1 to include a control parameter Λ = ρR, in which ρ represents the proportional reduction of the weed population, to give: Now, suppose that the requirements of agricultural production meant that the weed population was never allowed to build up to a level where density dependence [as described here by the (1 + aNt)−b term] seriously came into play and, further, that weed control was deemed unnecessary at low weed population densities. If K is a threshold density (K > 0) above which – on economic grounds – it has been decided that weed control is worthwhile, then, when N > K, and, when N ≤ K, This model was investigated by Wallinga & van Oijen (1997). They showed that the discontinuity imposed by the adoption of a discrete choice threshold for weed control gave rise to complex dynamics. Such a finding gives credence to the suggestion (Berryman & Millstein 1989) that chaotic dynamics may arise from human interventions (sometimes in pursuit of ‘control’) in agricultural systems. Weed population dynamics is not the only area of crop protection where such concerns arise. For example, Shaw (1994) discussed the implications of complex dynamics (induced by seasonal forcing) in models of plant disease, and Cavalieri & Kocak (1995) and Gonzalez-Andujar & Perry (1995) discussed the implications of complex dynamics for the biocontrol of the insect pest Ostrinia nubialis. Overall, the problem for population ecology was accurately summarized by Renshaw (1994). Failure to accept the properties of non-linear models of the form of equation 1– particularly where there is significant lagged density dependence, or where human intervention or seasonality causes discontinuities – may be misleading in a forecasting scenario. As mentioned earlier, the paucity of horizontal studies of weed population dynamics is attributable largely to the lack of appropriate time-series data. This lack, in turn, probably reflects a view of methodological difficulties voiced (doubtless on behalf of many others) by Cousens (1995), who asked: ‘How do we … distinguish in field data between environmentally driven fluctuations of an otherwise asymptotic behaviour and pure chaos driven by density dependence? We are back to the problem of interpreting horizontal density studies and away from the supposed advantages of vertical studies.’ However, Ellner & Turchin (1995) have argued that the separation of chaotic and stochastic dynamics in ecological systems, apart from being methodologically intractable, is unnecessary. The methods outlined by Ellner & Turchin (1995), based on statistical theory for parameter estimation in non-linear time-series models, characterize both the dynamic feedbacks regulating population behaviour and the ‘dynamic noise’ affecting how state variables change over time. Under this scheme, a combination of vertical and horizontal studies is required. For an entomological example, Cushing et al. (1998) combined models, experiments and statistical analysis of data to build up a predictive model. They developed a mathematical model that was impressively successful in describing and predicting the population dynamics of Tribolium castaneaum populations. Their results show convincingly that certain non-linear phenomena (complex dynamics) may occur. Their study demonstrates that mathematical models – even ‘simple’ mathematical models – are capable of providing accurate descriptions, explanations and predictions for the dynamics of biological populations. Weed management depends on a knowledge of weed biology (Bhowmik 1997), and models provide a basis for integrating this knowledge and studying qualitative scenarios (Gonzalez-Andujar & Fernandez-Quintanilla 1991). If we are to ‘demonstrate what dynamics actually occurs in nature’ (Cousens 1995) and apply the results in predictive weed management, we believe that the integration of vertical and horizontal approaches, as demonstrated by Cushing et al. (1998), represents a useful way forward.

Places of inquiry: Research and advanced education in modern universities

This article investigates the Cauchy problem for a stochastic partial differential-functional equation (SPDFE) of a special form, which models dynamic processes with memory under the influence of random perturbations. In particular, we examine the mathematical conditions ensuring the existence and uniqueness of the solution. The theoretical results are based on modern tools of stochastic analysis and functional differential calculus. Since analytical solutions to such equations are generally unavailable, the paper explores approaches for approximate numerical solutions. We describe the discretization of space and time, and techniques for approximating the functional (memory-dependent) terms using a historical buffer. Stochastic perturbations are modeled as space-time noise based on the Wiener process. We developed a Python-based software implementation using the Euler–Maruyama method to validate the theoretical results and provide a practical illustration of memory-driven dynamics. The considered equation models the evolution of a system under spatial diffusion, damping, memory effects (via past state dependence), and stochastic noise. For the numerical solution, we use discretized approximations of the memory integral as an average over a buffer of previous values. A graphical visualization of the spatiotemporal evolution is constructed, including a heatmap that shows how the system state u(t, x) «spreads» and fluctuates under the combined influence of memory and noise. The results are promising for further applications in the theory and practice of computational modeling of complex dynamical systems with memory and stochasticity. In particular, the developed approaches may be applied in modeling processes in physics (heat conduction with delay, diffusion in memory-structured media), biology and ecology (population dynamics or epidemic spread with incubation delays), financial mathematics (volatility depending on past states), and technical or information control systems with stochastic effects and signal delays.

The purpose of this work is a mathematical modeling of the distribution of nutrients taking into account the dynamics of phytoplankton populations and the influence of salinity and temperature. The goals of this work: the development of the mathematical model of phytoplankton populations dynamics, taking into account the transport and transformation of biogenic substances; obtaining stationary modes for the case of a spatially uniform distribution of substances; restoration of salinity and temperature fields; modeling of nutrient distribution taking into account the obtained results. Stationary regimes were obtained under the assumption that the development of phytoplankton is limited by a single nutrient - phosphorus, nitrogen or silicon. The modified Laplace equation was used to improve the order of accuracy of recovery of salinity and temperature fields. The distribution of pollutant (nitrogen), affecting the development of harmful blue-green algae, has been obtained.The purpose of this work is a mathematical modeling of the distribution of nutrients taking into account the dynamics of phytoplankton populations and the influence of salinity and temperature. The goals of this work: the development of the mathematical model of phytoplankton populations dynamics, taking into account the transport and transformation of biogenic substances; obtaining stationary modes for the case of a spatially uniform distribution of substances; restoration of salinity and temperature fields; modeling of nutrient distribution taking into account the obtained results. Stationary regimes were obtained under the assumption that the development of phytoplankton is limited by a single nutrient - phosphorus, nitrogen or silicon. The modified Laplace equation was used to improve the order of accuracy of recovery of salinity and temperature fields. The distribution of pollutant (nitrogen), affecting the development of harmful blue-green algae, has been obtained.