Discrete Stochastic Model Research Articles

Two-Stage Hyperelliptic Kalman Filter-Based Hybrid Fault Observer for Aeroengine Actuator under Multi-Source Uncertainty

An aeroengine faces multi-source uncertainty consisting of aeroengine epistemic uncertainty and the control system stochastic uncertainty during operation. This paper investigates actuator fault estimation under multi-source uncertainty to enhance the fault diagnosis capability of aero-engine control systems in complex environments. With the polynomial chaos expansion-based discrete stochastic model quantification, the optimal filter under multi-source uncertainty, the Hyperelliptic Kalman Filter, is proposed. Meanwhile, by treating actuator fault as unknown input, the Two-stage Hyperelliptic Kalman Filter (TSHeKF) is also proposed to achieve optimal fault estimation under multi-source uncertainty. However, considering that the biases of the model are often fixed for the individual, the TSHeKF-based fault estimation is robust and leads to inevitable conservativeness. By adding the additional estimation of the unknown deviation in state function caused by probabilistic system parameters, the hybrid fault observer (HFO) is proposed based on the TSHeKF and realizes conservativeness-reduced estimation for actuator fault under multi-source uncertainty. Numerical simulations show the effectiveness and optimality of the proposed HFO in state estimation, output prediction, and fault estimation for both single and multi-fault modes, when considering multi-source uncertainty. Furthermore, Monte Carlo experiments have demonstrated that the HFO-based optimal fault estimation is less conservative and more accurate than the Two-stage Kalman Filter and TSHeKF, providing better safety and more reliable aeroengine operation assurance.

A novel stochastic ProFiVaS model based on decomposition of stochastic Vasicek differential equation for modeling and simulating of financial indicators

The main purpose of this study is to develop a new discrete time stochastic ProFiVaS model based on decomposition of stochastic Vasicek differential equation which follows bouncing autoregressive AR1, with fixed variance and trend for modeling and simulating of international financial time series forecasting.This study offers the four discrete time stochastic models. The first model is determined as autoregressive integrated moving average-Arima1,1,1, and the parameter estimates of this model are found using the maximum likelihood method (MLM). Monte Carlo simulation is applied to the obtained parameters. This model is named MoCArima for short. Second, the MoCArima model whose parameters are estimated with particle swarm optimization (PSO) is determined as Proposed Monte Carlo (MC) Arima1,1,1, and is briefly named as ProMoCArima. The third model is determined as Fixed Variance Stochastic Model which has a bouncing autoregressive AR1 structure with constant variance and trend component. This model is briefly named as FiVaS. The parameter estimates are found using the MLM. The fourth model is determined as the Proposed Fixed Variance Stochastic Model. This model is briefly named as ProFiVaS. Structurally the same as the third model. The parameter estimates of both trend and stochastic parts of the FiVaS model are found by the PSO.Proposed models are applied to forecasting international different financial indicators to show its superiority and applicability. The performance and usage efficiency of the proposed four stochastic models are examined on a total of six different international financial data types, five of which are stock index data BIST100 (Türkiye), S&P500 (USA), DAX (Germany), FTSE100 (UK), NIKKEI225 (Japan), and one of which is the exchange rate EURO/USD. The ProFiVaS among all models provides the best performance on the all indices. The ProFiVaS can easily be extended to any real-world time series prediction requirements.The proposed models can be extended to all stationary and non-stationary linear or nonlinear autoregression models opening the door to modeling data types obtained from different sector fields. A part of the future plan of this work is to design a decision support system software that assigns a value of 1 when an investor needs to invest in a financial indicator, and 0 otherwise.

Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion.

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion; however, these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here, we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically inspired mechanisms and then deriving the reaction-diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, which we call a substrate, locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two-dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provide a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp fronts. Open-source Julia code to replicate all results in this work is available on GitHub.

Security Nanobot for Industrial Safety and Health in Sports using a Nanobot-Assisted Stochastic Discrete Choice Model

Security Nanobot for Industrial Safety and Health in Sports using a Nanobot-Assisted Stochastic Discrete Choice Model

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

A stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The proposed model’s finite time stability in probability is then investigated using a nonlinear feedback control approach at the interior Nash equilibrium. The stochastic Bellman theory is also used to explore the locally optimum control problem. Furthermore, bifurcation diagrams, time series, and the 0-1 test are used to investigate the chaotic dynamics of this model. Finally, numerical examples are given to illustrate the obtained results.

Quantifying Parameter Interdependence in Stochastic Discrete Models of Biochemical Systems.

Stochastic modeling of biochemical processes at the cellular level has been the subject of intense research in recent years. The Chemical Master Equation is a broadly utilized stochastic discrete model of such processes. Numerous important biochemical systems consist of many species subject to many reactions. As a result, their mathematical models depend on many parameters. In applications, some of the model parameters may be unknown, so their values need to be estimated from the experimental data. However, the problem of parameter value inference can be quite challenging, especially in the stochastic setting. To estimate accurately the values of a subset of parameters, the system should be sensitive with respect to variations in each of these parameters and they should not be correlated. In this paper, we propose a technique for detecting collinearity among models' parameters and we apply this method for selecting subsets of parameters that can be estimated from the available data. The analysis relies on finite-difference sensitivity estimations and the singular value decomposition of the sensitivity matrix. We illustrated the advantages of the proposed method by successfully testing it on several models of biochemical systems of practical interest.

Analysis of errors of the artificial horizon sensor based on vision system

The article discusses the features of the practical implementation of the artificial horizon sensor based on the onboard vision system. Proposed, developed on the basis of well-known applications, a variant of the algorithm for the operation of an unmanned aerial vehicle orientation video system. The problems of automatic detection and determination of the position of the horizon line on changing digital images that make up the video stream from the onboard digital camera are shown. The analysis of the factors influencing the accuracy of estimation of carrier orientation angles using the proposed system is carried out. The results of a practical study are presented, characterizing the degree of influence of the considered factors on the total error. A discrete stochastic mathematical model of an unmanned aerial vehicle orientation system based on an onboard vision system has been developed. The possibility of providing an acceptable level of accuracy of the orientation video system due to certain technical and algorithmic solutions is shown. The conclusion is made about the expediency of using this system in autonomous multisensor navigation systems for unmanned aerial vehicles.

Growth exponents reflect evolutionary processes and treatment response in brain metastases

Tumor growth is the result of the interplay of complex biological processes in huge numbers of individual cells living in changing environments. Effective simple mathematical laws have been shown to describe tumor growth in vitro, or simple animal models with bounded-growth dynamics accurately. However, results for the growth of human cancers in patients are scarce. Our study mined a large dataset of 1133 brain metastases (BMs) with longitudinal imaging follow-up to find growth laws for untreated BMs and recurrent treated BMs. Untreated BMs showed high growth exponents, most likely related to the underlying evolutionary dynamics, with experimental tumors in mice resembling accurately the disease. Recurrent BMs growth exponents were smaller, most probably due to a reduction in tumor heterogeneity after treatment, which may limit the tumor evolutionary capabilities. In silico simulations using a stochastic discrete mesoscopic model with basic evolutionary dynamics led to results in line with the observed data.

Дискретная стохастическая модель гидродинамики потока

For the mathematical description of hydrodynamic conditions in industrial equipment, idealized models are usually used. Upon receipt, a number of simplifying assumptions are made, which, on the one hand, facilitate the use, and on the other hand, the Appearance of the adequacy of the model. All typical models of flow structures are deterministic and continual. At the same time, it became known that the real situation arises in the process of considering possible factors. This trend leads to the need for a wider application of probabilistic approaches to modeling technological processes and apparatuses using modern digital technologies. This article cancels an attempt to create a hydrodynamic model using probabilistic cellular automata. In the model of occurrence, there is one reason for two flow velocities, a decision on the occurrence of a pressure drop, and the other is due to random walks of microvolumes of a moving medium. The described procedure for creating a model contains the results of its use. In particular, the results of modeling of motion trajectories in rare cases, the phenomena of their general movement and detection in rare zones were found. The article presents the results of a comparison of a discrete stochastic model with the types of a diffusion model, in terms of reflecting the physical essence of current flows, the possibilities of determining parameter models, and ease of use. The decisive aspects of the new model, its advantages and revolutions are shown. Possible areas of application of the obtained model. Under investigation are the results of simulation modeling using the proposed model, which reveal repeated results not only consistent with the classical approaches of hydrodynamics, but allow obtaining new data on the course of the processes under study.

Smart City Logistics on the Basis of Digital Tools for ESG Goals Achievement

The development of modern logistics systems requires state-of-the-art solutions for simultaneously achieving sustainable development goals and ambitious business targets. On this issue, the challenge of implementing digital technologies in social life, in particular in smart cities, deserves special attention. The diversified application of Industry 4.0 doctrine and digital shadow penetration to all fields of socioeconomic systems highlights the gaps in the design, control, and efficiency assessment of digital tools in the logistics of smart cities. Another challenge concerns the need to consider environmental, social, and governance (ESG) principles amid the deployment of harmonic digital tools within urban territories. All these issues require a complex methodological approach toward understanding the role of IT in the modern economy through an ESG prism. The article contains a contemporary literature review on the related topic and the conceptual framework of city logistics digitalization under ESG perspectives and constraints. The mathematical model proposed by the researchers enables a multidimensional design of digital solution applications within smart city logistics performance. The designed discrete stochastic model is eligible for scaling toward and the further development of variables other than the key ones mentioned above. The mathematical formalization of the proposed model considers the distribution of the limited budgeting of administrative branches within city logistics, highlighting the research relevance in connection with the ESG principles.

Experimental methods and mathematical modeling quantify and predict DUSP1 RNA expression dynamics in response to dexamethasone.

Overactivation of mitogen-activated protein kinase (MAPK) signaling pathways is key to multiple inflammatory responses, and synthetic glucocorticoids (GC), such as Dexamethasone (Dex), have long been used to treat inflammatory pathologies. Upon cell entry, Dex binds to the glucocorticoid receptor (GR), which initiates translocation to the nucleus. Nuclear GR then interacts with Glucocorticoid Regulatory Elements (GRE's) to promote transcription of anti-inflammatory genes including dual-specificity phosphatase 1 (DUSP1). In turn, DUSP1 encodes for the protein mitogen-activated protein kinase phosphatase 1 (MKP-1), which regulates the cell's anti-inflammatory response through dephosphorylation of the P38 and JUN N-terminal kinase (JNK) MAPK pathways. In this presentation, we combine single-cell measurements and discrete stochastic models to elucidate the spatiotemporal mechanisms by which Dex modulates GR localization and DUSP1 transcription. Using single-molecule inexpensive fluorescent in situ hybridization, we quantify the nascent transcription, spatial localization, and cellular heterogeneity of DUSP1 mRNA for hundreds of individual HeLa cells at 20 different time points following application of continuous 100 nM Dex stimulation. We observe a rapid increase in DUSP1 transcription sites (TS's) as early as 10-20 minutes, followed by a four-fold increase in expression of mature DUSP1 mRNA that peaks at 75-90 minutes and a temporary decrease in DUSP1 expression at 120-150 minutes post stimulation. We found that expression levels stay elevated during longer time course experiments, and high cellular heterogeneity is observed throughout the post-stimuli response. We used these experimental data to infer parameters and mechanisms for a discrete stochastic model that quantitatively reproduces the time-varying probability distributions for single-cell DUSP1 expression at all time points following Dex stimulation. Finally, we use this model inferred from DUSP1 expression to predict GR translocation dynamics and compare to direct measurement of GR localization dynamic using single-cell immunocytochemistry.

Experimental and Numerical (Fluent-VOF, k-ϵ, DPM) Study of Variation of Trap Efficiency of Irregular Hexagonal SIT (Sediment Invert Trap) for Particle Removal in Rectangular Open Drains and Sewers

At some locations along the length of open sewers and drains, sediment particles get deposited on the bottom bed, reducing hydraulic efficiency. A sediment invert trap (SIT) can be implemented on the bottom of open sewers and drains to trap sediment particles moving on the bed surface. Several investigators have conducted experimental and computational studies to understand the particle trapping behavior of invert traps of various shapes and depths under varying sediment and flow parameters. In experimental studies, previous investigators have used actual and artificial sediment particles; in computational analyses, spherical particles have been considered. The current study investigated the particle trapping behavior of an irregular hexagonal sediment invert trap (SIT) through experiments and two-dimensional (2D) numerical modeling. Seventy-two experiments were performed using actual sewage solid particles in an open rectangular channel with a bottom-fitted invert trap with multiple depths. Sixty numerical simulations were performed using ANSYS Fluent 2020 R1 computational fluid dynamics (CFD) software, considering spherical and nonspherical sewage solid particles. The velocity field was predicted using the volume of fluid (VOF) model combined with the realizable k-ϵ turbulence model. Particle trap efficiency was predicted using a stochastic discrete phase model (DPM). Trap efficiency varied significantly with depth of flow, invert trap depth, slot aperture size, and particle size and shape. Analysis of the simulated flow field showed that variation of turbulent kinetic energy above the trap’s slot aperture was also responsible for variations in trap efficiency values. Fluent simulations considering particles as nonspherical (using shape factors) agreed well with experimentally measured trap efficiency, with mean absolute percentage errors (MAPE) of 6.23%, 8.79%, and 13.77% for particle size ranges SS1, SS2, and SS3, respectively, with both slot apertures at all flow depths. The 2D-CFD study consistently overpredicted trap efficiencies compared to the experimental findings. With a fixed length and width of 0.32 and 0.15 m, respectively, the optimal depth of the irregular hexagonal SIT was found to be 0.65 m with slot aperture sizes of 0.15 and 0.03 m, whereas with slot aperture size of 0.15 m only, invert trap depths equal to 0.58, 0.43, and 0.38 m was found as optimum.

Cooperative Adaptive Cruise Control in a Mixed-Autonomy Traffic System: A Hybrid Stochastic Predictive Approach Incorporating Lane Change

This paper presents a stochastic and predictive control design approach for connected and automated vehicles (CAVs) in a mixed-autonomy traffic environment, where CAVs are able to react properly to uncertain maneuvers of human-driven vehicles (HVs). The proposed fully-automated cooperative adaptive cruise control (CACC) design leverages a discrete hybrid stochastic model predictive controller that automatically determines the vehicle's operating mode based on onboard sensors data and information received through vehicle-to-vehicle (V2V) communication. Operating modes include free following, warning, danger, emergency braking, and lane change. Although the controller mainly focuses on maintaining the desired velocity and distance among CAVs, it also allows HVs to perform lane-change maneuvers and merge into the platoon's lane when needed. In response to an HV's position in the lane and its probabilistic behavior, the controller may switch the CAV's operating mode to react accordingly. Considering free-following and emergency-braking modes leads to efficient and safe autonomous driving. Switching between warning, danger, and lane-change modes along with adjusting the steering angle to perform a lane-change maneuver, when needed, robustifies the platoon's performance against unexpected human-driven vehicle maneuvers. Simulation studies are conducted to validate the efficacy of the proposed control design approach. The performance of the proposed control design approach is also compared to a switching control using simulation studies.

A hybrid stochastic model predictive design approach for cooperative adaptive cruise control in connected vehicle applications

Wireless communication among connected and automated vehicles (CAVs) enables cooperative driving, particularly using cooperative adaptive cruise control, hence allowing CAVs to safely move closer to each other and improving traffic flow. However, reducing the gap between vehicles may cause collision, especially when a sudden deceleration in the vehicle platoon occurs. Furthermore, if some of the CAVs in the platoon lose communication, even for a short period, they may detect sudden changes in traffic with delay, and their reaction to avoid collision could be unsuccessful. Hence, an efficient emergency braking system can help preserve safety. This becomes even more important in high-speed driving, where a crash can put human lives in danger. This paper presents a discrete hybrid stochastic model predictive control approach to achieve a safe and efficient traffic system through CAV platooning. Three operational modes for vehicles are considered: free following, warning, and emergency braking. Each CAV in the free-following mode basically follows its preceding vehicle while enforcing maximum allowable deceleration in the emergency-braking mode. In the warning mode, the vehicle aims to slightly increase its headway and velocity difference from its predecessor to avoid possible danger. The warning/emergency-braking mode may be activated when the speed difference between a CAV and its preceding vehicle drops below a threshold. It is further assumed that vehicle distance sensing is subject to error. Each vehicle shares its current location, velocity, and future acceleration profile, calculated by solving a mixed-integer programming problem, with its follower vehicles. Simulation studies demonstrate the efficacy of the proposed control design approach compared to existing controllers in the literature in the presence of intermittent communication.

Estimation of the present status of the species based on the theoretical bounds of environmental noise intensity: An illustration through a big abundance data and simulation

Sibly et al. (2005) described that most species have a fundamental characteristic to follow the theta-logistic growth trait with the convex downward trend. The fundamental yardstick of this research work builds under the deterministic setup, whereas the involvement of the external noise in any growth system is inevitable. But, the involvement of external affairs in any species growth can not be well judged only through its density dependence; it requires a further assessment. So, we frame the theta-logistic model with the stochastic analog in two directions, i.e., the discrete and continuous setup. The analysis of the discrete stochastic model is manifested by the bifurcation analysis, which shows that the attainment of the chaotic regime enhances with the increase in noise intensity level. Although the role of chaos in species extinction is debatable, a literature survey suggests that chaos with stochasticity accelerates the extinction of species. Similarly, in the case of the continuous version, we performed a theoretical study on the stochastic theta-logistic model to provide a critical value of the noise intensity parameter. This threshold magnitude acts as the sustainability criterion of any species environmental tolerability. In this connection, we use the data of four major taxonomic groups, i.e., Bird, Insect, Mammal, and Fish, from the GPDD database and classifies the species based on environmental sensitivity. The highly sensitive species have a low tolerance level, associated with the small magnitude of environmental noise intensity parameter. Moreover, the simulation prediction model on these four taxonomic classes also shows that the overall extinction probability of the considered birds in our research work is almost negligible for the current time window.

Discrete stochastic models of SELEX: Aptamer capture probabilities and protocol optimization.

Antibodies are important biomolecules that are often designed to recognize target antigens. However, they are expensive to produce and their relatively large size prevents their transport across lipid membranes. An alternative to antibodies is aptamers, short (∼15-60 bp) oligonucleotides (and amino acid sequences) with specific secondary and tertiary structures that govern their affinity to specific target molecules. Aptamers are typically generated via solid phase oligonucleotide synthesis before selection and amplification through Systematic Evolution of Ligands by EXponential enrichment (SELEX), a process based on competitive binding that enriches the population of certain strands while removing unwanted sequences, yielding aptamers with high specificity and affinity to a target molecule. Mathematical analyses of SELEX have been formulated in the mass action limit, which assumes large system sizes and/or high aptamer and target molecule concentrations. In this paper, we develop a fully discrete stochastic model of SELEX. While converging to a mass-action model in the large system-size limit, our stochastic model allows us to study statistical quantities when the system size is small, such as the probability of losing the best-binding aptamer during each round of selection. Specifically, we find that optimal SELEX protocols in the stochastic model differ from those predicted by a deterministic model.

Social distancing and mask-wearing could avoid recurrent stay-at-home restrictions during COVID-19 respiratory pandemic in New York City

Stay-at-home restrictions such as closure of non-essential businesses were effective at reducing SARS-CoV-2 transmission in New York City (NYC) in the spring of 2020. Relaxation of these restrictions was desirable for resuming economic and social activities, but could only occur in conjunction with measures to mitigate the expected resurgence of new infections, in particular social distancing and mask-wearing. We projected the impact of individuals’ adherence to social distancing and mask-wearing on the duration, frequency, and recurrence of stay-at-home restrictions in NYC. We applied a stochastic discrete time-series model to simulate community transmission and household secondary transmission in NYC. The model was calibrated to hospitalizations, ICU admissions, and COVID-attributable deaths over March–July 2020 after accounting for the distribution of age and chronic health conditions in NYC. We projected daily new infections and hospitalizations up to May 31, 2021 under the different levels of adherence to social distancing and mask-wearing after relaxation of stay-at-home restrictions. We assumed that the relaxation of stay-at-home policies would occur in the context of adaptive reopening, where a new hospitalization rate of ≥ 2 per 100,000 residents would trigger reinstatement of stay-at-home restrictions while a new hospitalization rate of ≤ 0.8 per 100,000 residents would trigger relaxation of stay-at-home restrictions. Without social distancing and mask-wearing, simulated relaxation of stay-at-home restrictions led to epidemic resurgence and necessary reinstatement of stay-at-home restrictions within 42 days. NYC would have stayed fully open for 26% of the time until May 31, 2021, alternating reinstatement and relaxation of stay-at-home restrictions in four cycles. At a low (50%) level of adherence to mask-wearing, NYC would have needed to implement stay-at-home restrictions between 8% and 32% of the time depending on individual adherence to social distancing. At moderate to high levels of adherence to mask-wearing without social distancing, NYC would have needed to implement stay-at-home restrictions. In threshold analyses, avoiding reinstatement of stay-at-home restrictions required a minimum of 60% adherence to mask-wearing at 50% adherence to social distancing. With low adherence to mask-wearing and social distancing, reinstatement of stay-at-home restrictions in NYC was inevitable. High levels of adherence to social distancing and mask-wearing could have attributed to avoiding recurrent surges without reinstatement of stay-at-home restrictions.

Performance analysis of rectangular SIT (sediment invert trap) for stormwater drainage system

Abstract Deposition of solid particles in the stormwater sewers reduces the discharging capacity, causing inundation. A sediment invert trap (SIT) is an option that can be installed at the bottom of the stormwater sewer drain to intercept the flowing solid particles. In the present study performance of rectangular SIT were analyzed experimentally and computationally. Variation of particle trapping efficiency of rectangular SIT fitted at the bottom of the open channel flume has been studied under the interpretation of invert trap depth, flow depth, particle size, particle shape, and slot width. To predict the flow field and trap efficiency of a rectangular invert trap, 2D-VOF-DPM-CFD modelling has been carried out using ANSYS Fluent 2020 R1 software. For velocity field determination, the volume of fluid (VOF) model was used along with realizable k-є turbulence model. To predict particle trap efficiency, stochastic discrete phase model (DPM) was utilized. From experimental study and CFD modeling, it has been found that the particle trap efficiency of rectangular invert trap varied with change in the depth of invert trap, sediment size, shape factor, depth of flow and slot width. Consideration of particle shape in terms of shape factor in the modeling of solid-phase through DPM validated the CFD predicted results with those obtained experimentally with mean absolute percent error (MAPE) of 2.68%, 3.99% and 6.6% for sewer solid size ranges SS1, SS2, and SS3 respectively at all flow depths for both slot widths considered in this study.

Diffusion of New Products with Heterogeneous Consumers

Does a new product spread faster among heterogeneous or homogeneous consumers? We analyze this question using the stochastic discrete Bass model in which consumers may differ in their individual external influence rates [Formula: see text] and in their individual internal influence rates [Formula: see text]. When the network is complete and the heterogeneity is only manifested in [Formula: see text] or only in [Formula: see text], it always slows down the diffusion, compared with the corresponding homogeneous network. When, however, consumers are heterogeneous in both [Formula: see text] and [Formula: see text], heterogeneity slows down the diffusion in some cases but accelerates it in others. Moreover, the dominance between the heterogeneous and homogeneous adoption levels is global in time in some cases but changes with time in others. Perhaps surprisingly, global dominance between two networks is not always preserved under “additive transformations”, such as adding an identical node to both networks. When the network is not complete, the effect of heterogeneity depends also on its spatial distribution within the network.

Construction of COVID-19 Epidemic Prevention and Control and Public Health Emergency Response System Based on Discrete Stochastic Mathematical Model.

This research was aimed at exploring the construction and evaluation method of the comprehensive emergency response system for public health emergencies under the COVID-19 (coronavirus disease 2019) epidemic situation based on discrete stochastic mathematical model. The response of the Centers for Disease Control and Prevention (CDCP) of Taiyuan city in the COVID-19 epidemic situation was taken as an example. A new discrete stochastic COVID-19 epidemic spread mathematical model which integrated public health intervention and input cases was proposed. The model was parameterized by multisource data, and the impact of different flow patterns on the risk of secondary outbreak was analyzed. The advantages and disadvantages of its emergency system construction were analyzed. Additionally, the improvement measures and suggestions for the existing problems were proposed. Results suggested that there was only one specialized disease prevention and control institution in Taiyuan, and there were only 11 centers for disease prevention and control, accounting for 6.2% (11/177) of the total in Shanxi Province. Through the analysis, it was found that the current public health emergency response system in Taiyuan city had imperfect management coordination mechanism, incomplete plan type, serious shortage of public health personnel, poor information communication efficiency, insufficient early warning efficiency of the epidemic detection system, and weak logistics material security links. Therefore, it was proposed to establish a sound coordination system of emergency health management and vigorously promote the construction of emergency health management institutions. Thus, a public health emergency management system integrating management coordination system, plan system, emergency team building system, material reserve management, and other functions was formed. The application of discrete stochastic mathematical model suggests that intermittent population flow and effective isolation of infected people in transient population can effectively reduce the risk of secondary outbreak. The system analysis here also provides theoretical basis for improving the construction of public health emergency response system in Taiyuan.