Pricing Study on Two Kinds of Power Options in Jump-Diffusion Models with Fractional Brownian Motion and Stochastic Rate

In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the reset option with a single reset date and the phenomena of delta of the reset jumps existing in the reset option during the reset date are discussed. The closed-form formulae of pricing for two kinds of power options are derived in the end.

Comparative analysis of empirical and deep learning models for ionospheric sporadic E layer prediction

Sporadic E(Es)layers in the ionosphere are characterized by intense plasma irregularities in the E region at altitudes of 90-130 km.Because they can significantly influence radio communications and navigation systems,accurate forecasting of Es layers is crucial for ensuring the precision and dependability of navigation satellite systems.In this study,we present Es predictions made by an empirical model and by a deep learning model,and analyze their differences comprehensively by comparing the model predictions to satellite RO measurements and ground-based ionosonde observations.The deep learning model exhibited significantly better performance,as indicated by its high coefficient of correlation(r=0.87)with RO observations and predictions,than did the empirical model(r=0.53).This study highlights the importance of integrating artificial intelligence technology into ionosphere modelling generally,and into predicting Es layer occurrences and characteristics,in particular.

Aquaporin-4-IgG-seropositive neuromyelitis optica spectrum disorders:progress of experimental models based on disease pathogenesis

Neuromyelitis optica spectrum disorders are neuroinflammatory demyelinating disorders that lead to permanent visual loss and motor dysfunction.To date,no effective treatment exists as the exact causative mechanism remains unknown.Therefore,experimental models of neuromyelitis optica spectrum disorders are essential for exploring its pathogenesis and in screening for therapeutic targets.Since most patients with neuromyelitis optica spectrum disorders are seropositive for IgG autoantibodies against aquaporin-4,which is highly expressed on the membrane of astrocyte endfeet,most current experimental models are based on aquaporin-4-IgG that initially targets astrocytes.These experimental models have successfully simulated many pathological features of neuromyelitis optica spectrum disorders,such as aquaporin-4 loss,astrocytopathy,granulocyte and macrophage infiltration,complement activation,demyelination,and neuronal loss;however,they do not fully capture the pathological process of human neuromyelitis optica spectrum disorders.In this review,we summarize the currently known pathogenic mechanisms and the development of associated experimental models in vitro,ex vivo,and in vivo for neuromyelitis optica spectrum disorders,suggest potential pathogenic mechanisms for further investigation,and provide guidance on experimental model choices.In addition,this review summarizes the latest information on pathologies and therapies for neuromyelitis optica spectrum disorders based on experimental models of aquaporin-4-IgG-seropositive neuromyelitis optica spectrum disorders,offering further therapeutic targets and a theoretical basis for clinical trials.

Landslide Susceptibility Mapping Using RBFN-Based Ensemble Machine Learning Models

This study was aimed to prepare landslide susceptibility maps for the Pithoragarh district in Uttarakhand,India,using advanced ensemble models that combined Radial Basis Function Networks(RBFN)with three ensemble learning techniques:DAGGING(DG),MULTIBOOST(MB),and ADABOOST(AB).This combination resulted in three distinct ensemble models:DG-RBFN,MB-RBFN,and AB-RBFN.Additionally,a traditional weighted method,Information Value(IV),and a benchmark machine learning(ML)model,Multilayer Perceptron Neural Network(MLP),were employed for comparison and validation.The models were developed using ten landslide conditioning factors,which included slope,aspect,elevation,curvature,land cover,geomorphology,overburden depth,lithology,distance to rivers and distance to roads.These factors were instrumental in predicting the output variable,which was the probability of landslide occurrence.Statistical analysis of the models’performance indicated that the DG-RBFN model,with an Area Under ROC Curve(AUC)of 0.931,outperformed the other models.The AB-RBFN model achieved an AUC of 0.929,the MB-RBFN model had an AUC of 0.913,and the MLP model recorded an AUC of 0.926.These results suggest that the advanced ensemble ML model DG-RBFN was more accurate than traditional statistical model,single MLP model,and other ensemble models in preparing trustworthy landslide susceptibility maps,thereby enhancing land use planning and decision-making.

Exploiting fly models to investigate rare human neurological disorders

Rare neurological diseases,while individually are rare,collectively impact millions globally,leading to diverse and often severe neurological symptoms.Often attributed to genetic mutations that disrupt protein function or structure,understanding their genetic basis is crucial for accurate diagnosis and targeted therapies.To investigate the underlying pathogenesis of these conditions,researchers often use non-mammalian model organisms,such as Drosophila(fruit flies),which is valued for their genetic manipulability,cost-efficiency,and preservation of genes and biological functions across evolutionary time.Genetic tools available in Drosophila,including CRISPR-Cas9,offer a means to manipulate gene expression,allowing for a deep exploration of the genetic underpinnings of rare neurological diseases.Drosophila boasts a versatile genetic toolkit,rapid generation turnover,and ease of large-scale experimentation,making it an invaluable resource for identifying potential drug candidates.Researchers can expose flies carrying disease-associated mutations to various compounds,rapidly pinpointing promising therapeutic agents for further investigation in mammalian models and,ultimately,clinical trials.In this comprehensive review,we explore rare neurological diseases where fly research has significantly contributed to our understanding of their genetic basis,pathophysiology,and potential therapeutic implications.We discuss rare diseases associated with both neuron-expressed and glial-expressed genes.Specific cases include mutations in CDK19 resulting in epilepsy and developmental delay,mutations in TIAM1 leading to a neurodevelopmental disorder with seizures and language delay,and mutations in IRF2BPL causing seizures,a neurodevelopmental disorder with regression,loss of speech,and abnormal movements.And we explore mutations in EMC1 related to cerebellar atrophy,visual impairment,psychomotor retardation,and gain-of-function mutations in ACOX1 causing Mitchell syndrome.Loss-of-function mutations in ACOX1 result in ACOX1 deficiency,characterized by very-long-chain fatty acid accumulation and glial degeneration.Notably,this review highlights how modeling these diseases in Drosophila has provided valuable insights into their pathophysiology,offering a platform for the rapid identification of potential therapeutic interventions.Rare neurological diseases involve a wide range of expression systems,and sometimes common phenotypes can be found among different genes that cause abnormalities in neurons or glia.Furthermore,mutations within the same gene may result in varying functional outcomes,such as complete loss of function,partial loss of function,or gain-of-function mutations.The phenotypes observed in patients can differ significantly,underscoring the complexity of these conditions.In conclusion,Drosophila represents an indispensable and cost-effective tool for investigating rare neurological diseases.By facilitating the modeling of these conditions,Drosophila contributes to a deeper understanding of their genetic basis,pathophysiology,and potential therapies.This approach accelerates the discovery of promising drug candidates,ultimately benefiting patients affected by these complex and understudied diseases.

LoRa Sense:Sensing and Optimization of LoRa Link Behavior Using Path-Loss Models in Open-Cast Mines

The Internet of Things(IoT)has orchestrated various domains in numerous applications,contributing significantly to the growth of the smart world,even in regions with low literacy rates,boosting socio-economic development.This study provides valuable insights into optimizing wireless communication,paving the way for a more connected and productive future in the mining industry.The IoT revolution is advancing across industries,but harsh geometric environments,including open-pit mines,pose unique challenges for reliable communication.The advent of IoT in the mining industry has significantly improved communication for critical operations through the use of Radio Frequency(RF)protocols such as Bluetooth,Wi-Fi,GSM/GPRS,Narrow Band(NB)-IoT,SigFox,ZigBee,and Long Range Wireless Area Network(LoRaWAN).This study addresses the optimization of network implementations by comparing two leading free-spreading IoT-based RF protocols such as ZigBee and LoRaWAN.Intensive field tests are conducted in various opencast mines to investigate coverage potential and signal attenuation.ZigBee is tested in the Tadicherla open-cast coal mine in India.Similarly,LoRaWAN field tests are conducted at one of the associated cement companies(ACC)in the limestone mine in Bargarh,India,covering both Indoor-toOutdoor(I2O)and Outdoor-to-Outdoor(O2O)environments.A robust framework of path-loss models,referred to as Free space,Egli,Okumura-Hata,Cost231-Hata and Ericsson models,combined with key performance metrics,is employed to evaluate the patterns of signal attenuation.Extensive field testing and careful data analysis revealed that the Egli model is the most consistent path-loss model for the ZigBee protocol in an I2O environment,with a coefficient of determination(R^(2))of 0.907,balanced error metrics such as Normalized Root Mean Square Error(NRMSE)of 0.030,Mean Square Error(MSE)of 4.950,Mean Absolute Percentage Error(MAPE)of 0.249 and Scatter Index(SI)of 2.723.In the O2O scenario,the Ericsson model showed superior performance,with the highest R^(2)value of 0.959,supported by strong correlation metrics:NRMSE of 0.026,MSE of 8.685,MAPE of 0.685,Mean Absolute Deviation(MAD)of 20.839 and SI of 2.194.For the LoRaWAN protocol,the Cost-231 model achieved the highest R^(2)value of 0.921 in the I2O scenario,complemented by the lowest metrics:NRMSE of 0.018,MSE of 1.324,MAPE of 0.217,MAD of 9.218 and SI of 1.238.In the O2O environment,the Okumura-Hata model achieved the highest R^(2)value of 0.978,indicating a strong fit with metrics NRMSE of 0.047,MSE of 27.807,MAPE of 27.494,MAD of 37.287 and SI of 3.927.This advancement in reliable communication networks promises to transform the opencast landscape into networked signal attenuation.These results support decision-making for mining needs and ensure reliable communications even in the face of formidable obstacles.

Predictability Study of Weather and Climate Events Related to Artificial Intelligence Models

Conducting predictability studies is essential for tracing the source of forecast errors,which not only leads to the improvement of observation and forecasting systems,but also enhances the understanding of weather and climate phenomena.In the past few decades,dynamical numerical models have been the primary tools for predictability studies,achieving significant progress.Nowadays,with the advances in artificial intelligence(AI)techniques and accumulations of vast meteorological data,modeling weather and climate events using modern data-driven approaches is becoming trendy,where FourCastNet,Pangu-Weather,and GraphCast are successful pioneers.In this perspective article,we suggest AI models should not be limited to forecasting but be expanded to predictability studies,leveraging AI's advantages of high efficiency and self-contained optimization modules.To this end,we first remark that AI models should possess high simulation capability with fine spatiotemporal resolution for two kinds of predictability studies.AI models with high simulation capabilities comparable to numerical models can be considered to provide solutions to partial differential equations in a data-driven way.Then,we highlight several specific predictability issues with well-determined nonlinear optimization formulizations,which can be well-studied using AI models,holding significant scientific value.In addition,we advocate for the incorporation of AI models into the synergistic cycle of the cognition–observation–model paradigm.Comprehensive predictability studies have the potential to transform“big data”to“big and better data”and shift the focus from“AI for forecasts”to“AI for science”,ultimately advancing the development of the atmospheric and oceanic sciences.

Selection of Constitutive Models for As-Cast Low Alloyed Al-xSi-yCu Alloys

To guarantee the computational accuracy of the finite element model,the strain-compensated Arrhenius-type model,modified Fields-Backofen(m-FB)model and modified Zerilli-Armstrong(m-ZA)model were established to predict the hightemperature flow stress of as-cast low alloyed Al-0.5Cu,Al-1Si,and Al-1Si-0.5Cu.To determine the material constants of these three constitutive models,isothermal compression tests of the three aluminum alloys were carried out on a Gleeble-3800 thermal simulator.The prediction results of the constitutive model were compared with the experimental results to evaluate the prediction accuracy of the constitutive models,and to provide a basis for selecting the most suitable constitutive models(parameters)for the three alloys mentioned above.It is found that the strain-compensated Arrhenius model and m-ZA model can be regarded as the most suitable constitutive models for Al-0.5Cu and Al-1Si alloys,respectively,and these two constitutive models also can be applied to Al-1Si-0.5Cu alloy.However,the m-FB model can be applied to Al-0.5Cu,Al-1Si and Al-1Si-0.5Cu alloys only under high temperature and medium strain conditions.

Dynamic intelligent prediction approach for landslide displacement based on biological growth models and CNN-LSTM

Influenced by complex external factors,the displacement-time curve of reservoir landslides demonstrates both short-term and long-term diversity and dynamic complexity.It is difficult for existing methods,including Regression models and Neural network models,to perform multi-characteristic coupled displacement prediction because they fail to consider landslide creep characteristics.This paper integrates the creep characteristics of landslides with non-linear intelligent algorithms and proposes a dynamic intelligent landslide displacement prediction method based on a combination of the Biological Growth model(BG),Convolutional Neural Network(CNN),and Long ShortTerm Memory Network(LSTM).This prediction approach improves three different biological growth models,thereby effectively extracting landslide creep characteristic parameters.Simultaneously,it integrates external factors(rainfall and reservoir water level)to construct an internal and external comprehensive dataset for data augmentation,which is input into the improved CNN-LSTM model.Thereafter,harnessing the robust feature extraction capabilities and spatial translation invariance of CNN,the model autonomously captures short-term local fluctuation characteristics of landslide displacement,and combines LSTM's efficient handling of long-term nonlinear temporal data to improve prediction performance.An evaluation of the Liangshuijing landslide in the Three Gorges Reservoir Area indicates that BG-CNN-LSTM exhibits high prediction accuracy,excellent generalization capabilities when dealing with various types of landslides.The research provides an innovative approach to achieving the whole-process,realtime,high-precision displacement predictions for multicharacteristic coupled landslides.

Advancements and challenges in esophageal carcinoma prognostic models:A comprehensive review and future directions

In this article,we comment on the article published by Yu et al.By employing LASSO regression and Cox proportional hazard models,the article identified nine significant variables affecting survival,including body mass index,Karnofsky performance status,and tumor-node-metastasis staging.We firmly concur with Yu et al regarding the vital significance of clinical prediction models(CPMs),including logistic regression and Cox regression for assessment in esophageal carcinoma(EC).However,the nomogram's limitations and the complexities of integrating genetic factors pose challenges.The integration of immunological data with advanced statistics offers new research directions.High-throughput sequencing and big data,facilitated by machine learning,have revolutionized cancer research but require substantial computational resources.The future of CPMs in EC depends on leveraging these technologies to improve predictive accuracy and clinical application,addressing the need for larger datasets,patientreported outcomes,and regular updates for clinical relevance.

Reweighted Nadaraya-Watson estimation of jump-diffusion models

In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and asymptotic normality for the estimate of the second infinitesimal moment of continuous time models using the reweighted Nadaraya-Watson estimator to the true function.

Assessing the possibility of using large language models in ocular surface diseases

AIM:To assess the possibility of using different large language models(LLMs)in ocular surface diseases by selecting five different LLMS to test their accuracy in answering specialized questions related to ocular surface diseases:ChatGPT-4,ChatGPT-3.5,Claude 2,PaLM2,and SenseNova.METHODS:A group of experienced ophthalmology professors were asked to develop a 100-question singlechoice question on ocular surface diseases designed to assess the performance of LLMs and human participants in answering ophthalmology specialty exam questions.The exam includes questions on the following topics:keratitis disease(20 questions),keratoconus,keratomalaciac,corneal dystrophy,corneal degeneration,erosive corneal ulcers,and corneal lesions associated with systemic diseases(20 questions),conjunctivitis disease(20 questions),trachoma,pterygoid and conjunctival tumor diseases(20 questions),and dry eye disease(20 questions).Then the total score of each LLMs and compared their mean score,mean correlation,variance,and confidence were calculated.RESULTS:GPT-4 exhibited the highest performance in terms of LLMs.Comparing the average scores of the LLMs group with the four human groups,chief physician,attending physician,regular trainee,and graduate student,it was found that except for ChatGPT-4,the total score of the rest of the LLMs is lower than that of the graduate student group,which had the lowest score in the human group.Both ChatGPT-4 and PaLM2 were more likely to give exact and correct answers,giving very little chance of an incorrect answer.ChatGPT-4 showed higher credibility when answering questions,with a success rate of 59%,but gave the wrong answer to the question 28% of the time.CONCLUSION:GPT-4 model exhibits excellent performance in both answer relevance and confidence.PaLM2 shows a positive correlation(up to 0.8)in terms of answer accuracy during the exam.In terms of answer confidence,PaLM2 is second only to GPT4 and surpasses Claude 2,SenseNova,and GPT-3.5.Despite the fact that ocular surface disease is a highly specialized discipline,GPT-4 still exhibits superior performance,suggesting that its potential and ability to be applied in this field is enormous,perhaps with the potential to be a valuable resource for medical students and clinicians in the future.

How Do Deep Learning Forecasting Models Perform for Surface Variables in the South China Sea Compared to Operational Oceanography Forecasting Systems?

It is fundamental and useful to investigate how deep learning forecasting models(DLMs)perform compared to operational oceanography forecast systems(OFSs).However,few studies have intercompared their performances using an identical reference.In this study,three physically reasonable DLMs are implemented for the forecasting of the sea surface temperature(SST),sea level anomaly(SLA),and sea surface velocity in the South China Sea.The DLMs are validated against both the testing dataset and the“OceanPredict”Class 4 dataset.Results show that the DLMs'RMSEs against the latter increase by 44%,245%,302%,and 109%for SST,SLA,current speed,and direction,respectively,compared to those against the former.Therefore,different references have significant influences on the validation,and it is necessary to use an identical and independent reference to intercompare the DLMs and OFSs.Against the Class 4 dataset,the DLMs present significantly better performance for SLA than the OFSs,and slightly better performances for other variables.The error patterns of the DLMs and OFSs show a high degree of similarity,which is reasonable from the viewpoint of predictability,facilitating further applications of the DLMs.For extreme events,the DLMs and OFSs both present large but similar forecast errors for SLA and current speed,while the DLMs are likely to give larger errors for SST and current direction.This study provides an evaluation of the forecast skills of commonly used DLMs and provides an example to objectively intercompare different DLMs.

Evaluating large language models as patient education tools for inflammatory bowel disease:A comparative study

BACKGROUND Inflammatory bowel disease(IBD)is a global health burden that affects millions of individuals worldwide,necessitating extensive patient education.Large language models(LLMs)hold promise for addressing patient information needs.However,LLM use to deliver accurate and comprehensible IBD-related medical information has yet to be thoroughly investigated.AIM To assess the utility of three LLMs(ChatGPT-4.0,Claude-3-Opus,and Gemini-1.5-Pro)as a reference point for patients with IBD.METHODS In this comparative study,two gastroenterology experts generated 15 IBD-related questions that reflected common patient concerns.These questions were used to evaluate the performance of the three LLMs.The answers provided by each model were independently assessed by three IBD-related medical experts using a Likert scale focusing on accuracy,comprehensibility,and correlation.Simultaneously,three patients were invited to evaluate the comprehensibility of their answers.Finally,a readability assessment was performed.RESULTS Overall,each of the LLMs achieved satisfactory levels of accuracy,comprehensibility,and completeness when answering IBD-related questions,although their performance varies.All of the investigated models demonstrated strengths in providing basic disease information such as IBD definition as well as its common symptoms and diagnostic methods.Nevertheless,when dealing with more complex medical advice,such as medication side effects,dietary adjustments,and complication risks,the quality of answers was inconsistent between the LLMs.Notably,Claude-3-Opus generated answers with better readability than the other two models.CONCLUSION LLMs have the potential as educational tools for patients with IBD;however,there are discrepancies between the models.Further optimization and the development of specialized models are necessary to ensure the accuracy and safety of the information provided.

On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options under Regime-Switching Kou’s Jump-Diffusion Models

In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-differential equations(PIDEs).We show that this scheme is consistent,stable and monotone as the mesh sizes in space and time approach zero,hence it ensures the convergence to the solution of continuous problem.Finally,numerical experiments are performed to demonstrate the efficiency,accuracy and robustness of the proposed method.

Threshold reweighted Nadaraya-Watson estimation of jump-diffusion models

In this paper,we propose a new method to estimate the diffusion function in the jump-diffusion model.First,a threshold reweighted Nadaraya-Watson-type estimator is introduced.Then,we establish asymptotic normality for the estimator and conduct Monte Carlo simulations through two examples to verify the better finite-sampling properties.Finally,our estimator is demonstrated through the actual data of the Shanghai Interbank Offered Rate in China.

PRICING EUROPEAN OPTION IN A DOUBLE EXPONENTIAL JUMP-DIFFUSION MODEL WITH TWO MARKET STRUCTURE RISKS AND ITS COMPARISONS

Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.

Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

Evolution and Prospects of Foundation Models: From Large Language Models to Large Multimodal Models

Since the 1950s,when the Turing Test was introduced,there has been notable progress in machine language intelligence.Language modeling,crucial for AI development,has evolved from statistical to neural models over the last two decades.Recently,transformer-based Pre-trained Language Models(PLM)have excelled in Natural Language Processing(NLP)tasks by leveraging large-scale training corpora.Increasing the scale of these models enhances performance significantly,introducing abilities like context learning that smaller models lack.The advancement in Large Language Models,exemplified by the development of ChatGPT,has made significant impacts both academically and industrially,capturing widespread societal interest.This survey provides an overview of the development and prospects from Large Language Models(LLM)to Large Multimodal Models(LMM).It first discusses the contributions and technological advancements of LLMs in the field of natural language processing,especially in text generation and language understanding.Then,it turns to the discussion of LMMs,which integrates various data modalities such as text,images,and sound,demonstrating advanced capabilities in understanding and generating cross-modal content,paving new pathways for the adaptability and flexibility of AI systems.Finally,the survey highlights the prospects of LMMs in terms of technological development and application potential,while also pointing out challenges in data integration,cross-modal understanding accuracy,providing a comprehensive perspective on the latest developments in this field.

The relationship between compartment models and their stochastic counterparts:A comparative study with examples of the COVID-19 epidemic modeling

Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochastic models is not well understood.The present study aimed to address this gap by conducting a comparative study using the susceptible,exposed,infectious,and recovered(SEIR)model and its extended CMs from the coronavirus disease 2019 modeling literature.We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations.Based on this equivalence,we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment.The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics.However,it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs.Additionally,we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents.This model offered a balance between computational efficiency and accuracy.The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling.Furthermore,the results had implications for the development of hybrid models that integrated the strengths of both frameworks.Overall,the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.