Deterministic Model Research Articles

A deterministic fluid model for production and energy mode control of a single machine

Improving machines’ energy efficiency through dynamic energy mode control to meet demand requirements with minimal energy consumption is a promising approach. This study considers a machine operating in working, idle, off, and warmup energy modes with different energy consumption in each mode. A deterministic fluid model is developed to analyze an energy mode control policy that determines when to keep the machine working, off or idle, and switch to other modes based on the inventory/backlog level to minimize the total energy, inventory, and backlog costs. This approach facilitates the derivation of closed-form expressions for the optimal thresholds and the associated costs. This modeling approach allows us to prove that a policy that operates the machine between the working and off modes or the working and idle modes is always better than a hybrid policy that operates the machine in working, off, and idle modes simultaneously. We use the solution of the deterministic fluid model to propose an approximate policy for machines with stochastic production, warmup, and demand processes. We compare the results of the proposed approximation method with the optimal solution of a stochastic system where the production and warmup times are exponential and the demand inter-arrival times have Erlang distribution. The optimal solution for the stochastic system is determined by solving a Markovian Decision Process (MDP). Our numerical experiments show that the proposed approximation method predicts the optimal policy type for the stochastic case with a 89.3% accuracy, and the average error between the optimal cost and the cost obtained with the approximation method is 1.37% for 729 different cases tested. Furthermore, the computational efficiency of the proposed approximation is around 250 times better than the effort to determine the optimal policy using an MDP approach. We propose this approximation method where the control parameters are given in closed form as an easy-to-implement and effective policy to control energy modes to minimize the total energy, inventory, and backlog costs. Furthermore, we present the deterministic fluid modeling approach as a versatile approach to analyze energy mode control problems.

On a Symmetry-Based Structural Deterministic Fractal Fractional Order Mathematical Model to Investigate Conjunctivitis Adenovirus Disease

In the last few years, the conjunctivitis adenovirus disease has been investigated by using the concept of mathematical models. Hence, researchers have presented some mathematical models of the mentioned disease by using classical and fractional order derivatives. A complementary method involves analyzing the system of fractal fractional order equations by considering the set of symmetries of its solutions. By characterizing structures that relate to the fundamental dynamics of biological systems, symmetries offer a potent notion for the creation of mechanistic models. This study investigates a novel mathematical model for conjunctivitis adenovirus disease. Conjunctivitis is an infection in the eye that is caused by adenovirus, also known as pink eye disease. Adenovirus is a common virus that affects the eye’s mucosa. Infectious conjunctivitis is most common eye disease on the planet, impacting individuals across all age groups and demographics. We have formulated a model to investigate the transmission of the aforesaid disease and the impact of vaccination on its dynamics. Also, using mathematical analysis, the percentage of a population which needs vaccination to prevent the spreading of the mentioned disease can be investigated. Fractal fractional derivatives have been widely used in the last few years to study different infectious disease models. Hence, being inspired by the importance of fractal fractional theory to investigate the mentioned human eye-related disease, we derived some adequate results for the above model, including equilibrium points, reproductive number, and sensitivity analysis. Furthermore, by utilizing fixed point theory and numerical techniques, adequate requirements were established for the existence theory, Ulam–Hyers stability, and approximate solutions. We used nonlinear functional analysis and fixed point theory for the qualitative theory. We have graphically simulated the outcomes for several fractal fractional order levels using the numerical method.

A rational ansatz for the approximation of Koopman eigenfunctions

AbstractKoopman operator theory offers a basis for the systematic transformation and linearization of complex dynamical systems. We propose a method to approximate eigenfunctions of the Koopman operator for sufficiently smooth, deterministic and autonomous dynamical systems with hyperbolic fixed points in an equation‐based context. Approximations of the eigenfunctions are obtained in form of a rational ansatz whose coefficients are determined by minimizing a residual through a bi‐quadratic optimization problem. In addition, we consider an extension of the Hartman‐Grobman theorem, which was first proposed by Lan and Mezić in 2013, as a linear constraint. The implementation for a damped pendulum shows that the approach works in general, however, the optimization problem is non‐convex and thus sensible w. r. t. initial conditions, and increases proportional to the number of ansatz functions to the power of four.

Modeling the Transmission Dynamics of the Ebola Virus: Effects of Quarantine and Vaccination

Quarantine and vaccination of individuals suspected of exposure to infectious agents are fundamental public health strategies that have historically been employed to mitigate the transmission of contagious diseases within human populations. This study introduced a modified SEIVQRD deterministic model to evaluate the population-level effects of quarantine and vaccination on individuals potentially exposed to the Ebola virus. The study showed that the Model exhibits backward bifurcation when . This implies that even when the reproductive number An unstable endemic and a stable disease-free equilibrium can coexist in less than one. This phenomenon arises from imperfect quarantine and indicates that while is necessary for adequate infection control; it is no longer sufficient and creates additional challenges for effectively controlling Ebola. Furthermore, the sensitivity analysis revealed that the quarantine effectiveness parameter and the parameter related to the isolation of vulnerable individuals had less influence on the incidence of new Ebola cases. However, vaccinating non-quarantined susceptible individuals significantly affects the infection burden and can lower the reproductive value to less than one. Overall, the Model emphasizes the critical role of vaccination in reducing Ebola virus transmission. Although quarantine measures alone may not be sufficient, their combination with vaccination can significantly reduce infection rates.

Application of the PSI cycle check-up methodology for full-core Monte Carlo simulations verified using pin power estimates and validated for hot zero power conditions

Monte Carlo (MC) based neutron transport codes provide high-fidelity numerical solutions to problems beyond the modelling capabilities of conventional core simulation methods. However, performing core-follow calculations with MC codes remains challenging due to the necessity of incorporating thermal-hydraulic feedback and generating evolved fuel composition for the cycle of interest by taking into account the entire irradiation history of loaded fuel assemblies over previous cycles. Nevertheless, at PSI, the neutronic version of a cycle check-up methodology (CHUP) is under development to address this challenge. This methodology involves extracting operating conditions and nuclide compositions from validated reference deterministic core-follow models (CASMO5/SIMULATE5/SNF), subsequently generating MC neutron transport models for selected operating points. This article presents the verification and validation performed for a hot zero power operating condition of a Swiss pressurised water reactor using the updated CHUP methodology, which automates information extraction from reference core models to minimise human intervention. The MC models were verified by assessing their deviation from criticality, consistently found to be supercritical within the [10,60] pcm range. Additionally, radial relative power distribution verification yield deviations in the [−5,4] % range compared to validated nodal results. Finally, additional validation was performed using start-up measurements from two successive cycles. Eight MC models were found to be subcritical, on average by 51 pcm, with a standard deviation of 25 pcm.

Stationary distribution of a stochastic generalized SIRI epidemic model with reinfection and relapse

In this paper, we propose and investigate the stochastic SIRI epidemic model with two generalized incidence rate functions. We firstly study the existence and uniqueness of the globally positive solution to the stochastic SIRI model with positive initial value. Then we obtain sufficient conditions for the extinction of the disease in the stochastic epidemic model, and find that the large noise can make the disease die out exponentially. Meanwhile, we obtain that the solution to the stochastic model has a unique stationary distribution when R0s˜ is greater than one. Our results show that the intensity of white noise can affect the dynamical behaviors of the model. Finally, we use numerical simulation to illustrate theoretical results, and apply both the stochastic and deterministic models to analyze the outbreak of COVID-19 epidemic in Serbia.

Long-term waning of vaccine-induced immunity to measles in England: a mathematical modelling study

Among people infected with measles in England between 2010 and 2019, the proportion of cases who had previously received two doses of vaccine has increased, especially among young adults. Possible explanations include rare infections in vaccinated individuals who did not gain immunity upon vaccination, made more common because fewer individuals in the population were born in the endemic era, before vaccination was introduced, and exposed as part of endemic transmission, or the waning of vaccine-induced immunity, which would present new challenges for measles control in near-elimination settings. We aimed to evaluate whether measles dynamics observed in England between 2010 and 2019 were in line with a waning of vaccine-induced immunity. We used a compartmental mathematical model stratified by age group, region, and vaccine status, fitted to individual-level case data reported in England from 2010 to 2019 and collected by the UK Health Security Agency. The deterministic model was fitted using Monte Carlo Markov Chains under three scenarios: without the waning of vaccine-induced immunity, with waning depending on time since vaccination, and with waning depending on time since vaccination, starting in 2000. We generated stochastic simulations from the fitted parameter sets to evaluate which scenarios could replicate the transmission dynamics observed in vaccinated cases in England. The scenario without waning overestimated the number of one-dose recipients among measles cases, and underestimated the number of two-dose recipients among cases older than 15 years (median 75 cases [95% simulation interval (SI) 44-124] in simulations without waning, 196 [95% SI 122-315] in simulations when waning was included, 188 [95% SI 118-301] in simulations when waning started in 2000, and 202 observed cases). The number of onward transmissions from vaccinated cases was 83% (95% credible interval 72-91%) of the number of transmissions from unvaccinated cases. The estimated waning rate was slow (0·039% per year of age; 95% credible interval 0·034-0·044% per year in the best-fitting scenario with waning starting in 2000), but sufficient to increase measles burden. Measles case dynamics in England are consistent with scenarios assuming the waning of vaccine-induced immunity. Since measles is highly infectious, slow waning leads to a heightened burden in outbreaks, increasing the number of measles cases in people who are both vaccinated and unvaccinated. Our findings show that although the vaccine remains highly protective against measles infections for decades and most transmission is connected to people who are unvaccinated, breakthrough infections are increasingly frequent for individuals aged 15 years and older who have been vaccinated twice. National Institute for Health and Care Research and Wellcome Trust.

Characterisation and simulated evaluation of electricity management strategies for Prosumers, Prosumagers, and other end-users

ABSTRACT Distributed photovoltaic generation has been raised as a dependable electricity substitute for implementing a decarbonised energy transition. The dynamics of PV systems with battery storage have led to new electricity end-user classifications that select their electricity systems and resources wisely, i.e. Prosumers and Prosumagers. This work presents a technical and economic assessment to analyse the effect of decision-making independent end-users and electricity management strategies through a novel time-discrete deterministic simulation model. The end-user's choice of battery storage technology and their approach to electricity management emerge as pivotal factors influencing their strategic decisions. Adopting a prosumer strategy, such as storing and selling surplus self-production, reduces the Levelized Cost of Energy (LCOE), benefiting the end-user economically. Notably, the most effective battery storage technology may only sometimes be the one that is most readily available in the market. These findings enhance our understanding of novel end-user types and underscore the practical implications of their evolutionary shift towards independence.

Dynamics analysis of a delayed stochastic SIRS epidemic model with a nonlinear incidence rate

. This article proposes a stochastic delayed SIRS epidemic model with nonlinear incidence to describe disease transmission in a stochastic environment. First, it proves that the model has a unique global positive solution and derives sufficient conditions for the extinction and persistence of the epidemic in the population under appropriate conditions. Then, by constructing suitable Lyapunov functions, the asymptotic behavior of the model around the disease-free equilibrium and endemic equilibrium points of the deterministic model is analyzed, and it is concluded that under certain conditions, the solution of the stochastic system randomly oscillates around these two equilibrium points. Finally, several numerical examples are provided to validate the theoretical results, illustrating the significant impact of stochastic perturbations and time delays on disease control.

Free Will and the Paradox of Predictability

In recent literature there has been increased interest in the so-called “paradox of predictability” (PoP) which purportedly shows that a deterministic universe is fundamentally unpredictable, even if its initial state and governing laws are known perfectly. This ostensible conclusion has been used to support compatibilism, the thesis that determinism is compatible with free will: supposedly, the PoP reveals that the nature of determinism is misunderstood and actually allows freedom, hence also free will. The present paper aims to disprove this conclusion and show that the PoP has absolutely no implication concerning the predictability of deterministic systems and the nature of determinism. Its paradoxy arises from a confusion between mental and physical notions in its formulation (the PoP tacitly premises a mental arbiter with respect to whom notions such as prediction and signification have meaning) and disappears once it is expressed in purely physical language. Ultimately, the PoP demonstrates not that prediction is impossible under determinism, but merely the obvious fact that it is impossible to predict while simultaneously acting so as to disprove one’s own prediction. The related issue of the impossibility of self-prediction is also discussed.

Bifurcation analysis and exploration of noise-induced transitions of a food chain model with Allee effect

Seeking shelter from threats is a widespread instinct across species, specially employed by prey to avoid direct confrontations with predators. The present investigation centers on a three-species food chain model wherein the basal prey, characterized by logistic growth, seeks refuge to evade the intermediate predator, while the intermediate predator, in turn, seeks refuge to avoid encounters with the top predator. Additionally, our model assumes that the presence of the top predator induces a mate-finding Allee effect among the intermediate predator. We investigate how varying levels of refuge, along with other critical parameters such as the reproduction rate of the basal prey and the natural mortality rate of the top predator, influence system’s dynamics within the biparametric planes. Our model displays multistability and undergoes transcritical, saddle–node, Bogdanov–Takens and cusp bifurcations across different parameters. Moreover, the external environmental noise can induce interesting dynamics in the predator–prey system, resulting in noise-induced frequent transitions between distinct interior attractors or from interior to axial attractors. This phenomenon is particularly notable in scenarios where the deterministic model exhibits tristability. In summary, our findings offer potential new avenues for developing control strategies within the realm of community ecology in constant as well as fluctuating environments.

Insights into the occurrence, distribution and dissipation of widespread agrochemicals in celery agrosystems for joint risk assessment

Elucidating exposure risks associated with the most widely used agrochemicals and their metabolites in celery agrosystems are vital for food safety and human health. The occurrence, distribution, dissipation and metabolism of imidacloprid (IMI), acetamiprid (ACE), thiamethoxam (THM) and difenoconazole (DIF) in celery tissues reflected by initial depositions, uptake characteristics, half-lives, concentration variations. DIF exhibited unacceptable ecological risk to soil organisms under multi-risk evaluation models, including toxicity exposure ratio, risk quotient, and BITSSD model. The joint dietary risks of target pesticides were 37.273–647.454% and 0.400–2522.016% based on deterministic and probabilistic models, with non-carcinogenic risks of 30.207–85.522% and 1.229–2524.662%, respectively. Children aged 1–6 years suffered the highest exposure, with the leaves posing higher risk than other tissues. Long-term exposure risks should be continuously assessed for ecological sustainability and human health, given the widespread usage and cumulative effects of target pesticides, especially for rural children.

Neural downscaling for complex systems: from large-scale to small-scale by neural operator

Researchers have long been working on interpreting and predicting the dynamics of complex systems in various fields. Conventional methods including full-scale simulations and reduced-order models are used to solve related problems, but often yield unsatisfactory results in terms of precision and computational efficiency. This is primarily due to the challenges posed by simulating small-scale dynamics. An alternative consideration is to leverage well-represented and readily accessible large-scale dynamics to assist small-scale modelling. This paper proposes a novel methodology, named as Neural Downscaling (ND), that effectively captures small-scale dynamics within a complementary subspace from corresponding large-scale dynamics well-represented in a low-dimensional space. The framework of ND integrates neural operator techniques with the principles of inertial manifold and nonlinear Galerkin theory. The effectiveness and efficiency of ND are demonstrated in the complex systems governed by Kuramoto–Sivashinsky and Navier–Stokes equations. Being an unprecedentedly deterministic model targeted at general small-scale dynamics, ND sheds light on the intricate spatiotemporal nonlinear dynamics of complex systems and reveals how small-scale dynamics are interacting with large-scale dynamics.

Machine learning and deep learning models based grid search cross validation for short-term solar irradiance forecasting

In late 2023, the United Nations conference on climate change (COP28), which was held in Dubai, encouraged a quick move from fossil fuels to renewable energy. Solar energy is one of the most promising forms of energy that is both sustainable and renewable. Generally, photovoltaic systems transform solar irradiance into electricity. Unfortunately, instability and intermittency in solar radiation can lead to interruptions in electricity production. The accurate forecasting of solar irradiance guarantees sustainable power production even when solar irradiance is not present. Batteries can store solar energy to be used during periods of solar absence. Additionally, deterministic models take into account the specification of technical PV systems and may be not accurate for low solar irradiance. This paper presents a comparative study for the most common Deep Learning (DL) and Machine Learning (ML) algorithms employed for short-term solar irradiance forecasting. The dataset was gathered in Islamabad during a five-year period, from 2015 to 2019, at hourly intervals with accurate meteorological sensors. Furthermore, the Grid Search Cross Validation (GSCV) with five folds is introduced to ML and DL models for optimizing the hyperparameters of these models. Several performance metrics are used to assess the algorithms, such as the Adjusted R2 score, Normalized Root Mean Square Error (NRMSE), Mean Absolute Deviation (MAD), Mean Absolute Error (MAE) and Mean Square Error (MSE). The statistical analysis shows that CNN-LSTM outperforms its counterparts of nine well-known DL models with Adjusted R2 score value of 0.984. For ML algorithms, gradient boosting regression is an effective forecasting method with Adjusted R2 score value of 0.962, beating its rivals of six ML models. Furthermore, SHAP and LIME are examples of explainable Artificial Intelligence (XAI) utilized for understanding the reasons behind the obtained results.

Optimizing Dry Port Locations: A Comparative Analysis of Deterministic, Stochastic, and Robust Models

The increasing international maritime transportation of freight has caused a huge operation in important ports, which are often established near cities and therefore do not have enough room for expanding the operations. This causes long delays and poor productivity in ports. The construction of dry ports has been proposed as a suitable solution to mitigate the problems. A dry port is an inland intermodal terminal directly connected to a seaport by road or rail, where importers and exporters can clear their cargo through customs and handle other shipping formalities. Selecting the right place for the establishment of dry ports has a significant impact on the time and costs of transportation in the network, as well as environmental consequences. In this research, to determine the optimal location of dry ports among the potential locations, three mathematical models as deterministic, stochastic, and robust with three objectives of minimizing the maximum transportation time in the entire network, environmental pollutants, and transportation costs are presented, which simultaneously specify the required number of dry ports in the network and the optimal place to build them. The presented models have been implemented for data related to 30 million bills of lading in a 10-year period in Iran with four major ports and 400 cities. Both deterministic and non-deterministic approaches reveal a preference not to build a dry port in the first optimal solution. However, in the following desirable answers, different answers have been suggested. According to the sensitivity analysis performed by making changes in the fuel price situation or the existing rail network, the model introduces several potential points for the construction of dry ports. The results of this model show that, with the construction of dry ports, despite the increase in overall costs of the network because of the construction of dry ports, operation, and storage in them, the amount of greenhouse gas emissions will decrease significantly.

Requirements for the Development and Operation of a Freeze-Up Ice-Jam Flood Forecasting System

This article provides a comprehensive overview of ice-jam flood forecasting methodologies applicable to rivers during freezing. It emphasizes the importance of understanding river ice processes and fluvial geomorphology for developing a freeze-up ice-jam flood forecasting system. The article showcases a stochastic modelling approach, which involves simulating a deterministic river ice model multiple times with varying parameters and boundary conditions. This approach has been applied to the Exploits River at Badger in Newfoundland, Canada, a river that has experienced several freeze-up ice-jam floods. The forecasting involves two approaches: predicting the extent of the ice cover during river freezing and using an ensemble method to determine backwater flood level elevations. Other examples of current ice-jam flood forecasting systems for the Kokemäenjoki River (Pori, Finland), Saint John River (Edmundston, NB, Canada), and Churchill River (Mud Lake, NL, Canada) that are operational are also presented. The text provides a detailed explanation of the processes involved in river freeze-up and ice-jam formation, as well as the methodologies used for freeze-up ice-jam flood forecasting. Ice-jam flood forecasting systems used for freeze-up were compared to those employed for spring breakup. Spring breakup and freeze-up ice-jam flood forecasting systems differ in their driving factors and methodologies. Spring breakup, driven by snowmelt runoff, typically relies on deterministic and probabilistic approaches to predict peak flows. Freeze-up, driven by cold temperatures, focuses on the complex interactions between atmospheric conditions, river flow, and ice dynamics. Both systems require air temperature forecasts, but snowpack data are more crucial for spring breakup forecasting. To account for uncertainty, both approaches may employ ensemble forecasting techniques, generating multiple forecasts using slightly different initial conditions or model parameters. The objective of this review is to provide an overview of the current state-of-the-art in ice-jam flood forecasting systems and to identify gaps and areas for improvement in existing ice-jam flood forecasting approaches, with a focus on enhancing their accuracy, reliability, and decision-making potential. In conclusion, an effective freeze-up ice-jam flood forecasting system requires real-time data collection and analysis, historical data analysis, ice jam modeling, user interface design, alert systems, and integration with other relevant systems. This combination allows operators to better understand ice jam behavior and make informed decisions about potential risks or mitigation measures to protect people and property along rivers. The key findings of this review are as follows: (i) Ice-jam flood forecasting systems are often based on simple, empirical models that rely heavily on historical data and limited real-time monitoring information. (ii) There is a need for more sophisticated modeling techniques that can better capture the complex interactions between ice cover, water levels, and channel geometry. (iii) Combining data from multiple sources such as satellite imagery, ground-based sensors, numerical models, and machine learning algorithms can significantly improve the accuracy and reliability of ice-jam flood forecasts. (iv) Effective decision-support tools are crucial for integrating ice-jam flood forecasts into emergency response and mitigation strategies.

Adolescent vaping behaviours: Exploring the dynamics of a social contagion model

Vaping, or the use of electronic cigarettes (e-cigarettes), is an ongoing issue for public health. The rapid increase in e-cigarette usage, particularly among adolescents, has often been referred to as an epidemic. Drawing upon this epidemiological analogy between vaping and infectious diseases as a theoretical framework, we present a deterministic compartmental model of adolescent e-cigarette smoking which accounts for social influences on initiation, relapse, and cessation behaviours. We use results from a sensitivity analysis of the model’s parameters on various response variables to identify key influences on system dynamics and simplify the model into one that can be analysed more thoroughly. We identify a single feasible endemic equilibrium for the proportion of smokers that decreases as social influence on cessation increases. Through steady state and stability analyses, as well as simulations of the model, we conclude that social influences from and on temporary quitters are not important in overall model dynamics, and that social influences from permanent quitters can have a significant impact on long-term system dynamics. In particular, we show that social influence on cessation can induce persistent recurrent smoking outbreaks.

Optimal control and cost-effectiveness analysis of nonlinear deterministic Zika virus model

Optimal control and cost-effectiveness analysis of nonlinear deterministic Zika virus model

Arsenic and cadmium in the hydrological cycle and soil in a maquis broadleaved evergreen forest stand in Greece. Sources of some uncertainties

ABSTRACT The concentrations and fluxes of arsenic (As) and cadmium (Cd) were examined in the hydrological cycle, litterfall and soils in a maquis broadleaved evergreen forest stand in western Greece. The concentrations of the metals in the hydrological cycle ranged from 0.076 to 0.306 μg L−1 and 0.040–0.050 μg L−1 for As and Cd, respectively. It was found that the enrichment of As in the atmosphere was both due to suspended geogenic material and long range transfer, whereas for Cd the long range transfer was the predominant way for deposition. Two models were assessed to find the volumes of percolation water to compare the fluxes with the estimated ones derived from soil solution measurements. The daily deterministic forest-hydrological model (WBS3) was found to perform better than the physically based 1D semi-distributed soil-plant-atmosphere model (BROOK90). When calculating the total amounts of the heavy metals in soils, the statistical uncertainty derived from every soil layer has to be taken into account. The residence time of Cd in the forest floor (L + FH) of the soils was found 6.4 years, whereas that of As 36.3 years. This difference shows the mobility of Cd in comparison to As in the soils of the area.

Modeling different strategies towards control of lung cancer: leveraging early detection and anti-cancer cell measures

The global population has encountered significant challenges throughout history due to infectious diseases. To comprehensively study these dynamics, a novel deterministic mathematical model, TCD I L 2 Z, is developed for the early detection and treatment of lung cancer. This model incorporates I L 2 cytokine and anti-PD-L1 inhibitors, enhancing the immune system’s anticancer response within five epidemiological compartments. The TCD I L 2 Z model is analyzed qualitatively and quantitatively, emphasizing local stability given the limited data-a critical component of epidemic modeling. The model is systematically validated by examining essential elements such as equilibrium points, the reproduction number ( R 0 ), stability, and sensitivity analysis. Next-generation techniques based on R 0 that track disease transmission rates across the sub-compartments are fed into the system. At the same time, sensitivity analysis helps model how a particular parameter affects the dynamics of the system. The stability on the global level of such therapy agents retrogrades individuals with immunosuppression or treated with I L 2 and anti-PD-L1 inhibitors admiring the Lyapunov functions’ applications. NSFD scheme based on the implicit method is used to find the exact value and is compared with Euler’s method and RK4, which guarantees accuracy. Thus, the simulations were conducted in the MATLAB environment. These simulations present the general symptomatic and asymptomatic consequences of lung cancer globally when detected in the middle and early stages, and measures of anticancer cells are implemented including boosting the immune system for low immune individuals. In addition, such a result provides knowledge about real-world control dynamics with I L 2 and anti-PD-L1 inhibitors. The studies will contribute to the understanding of disease spread patterns and will provide the basis for evidence-based intervention development that will be geared toward actual outcomes.