Discrete-time Model Research Articles

Development of a Microsimulation Model to Project the Future Prevalence of Childhood Cancer in Ontario, Canada.

Estimates of the future prevalence of childhood cancer are informative for health system planning but are underutilized. We describe the development of a pediatric oncology microsimulation model for prevalence (POSIM-Prev) and illustrate its application to produce projections of incidence, survival, and limited-duration prevalence of childhood cancer in Ontario, Canada, until 2040. POSIM-Prev is a population-based, open-cohort, discrete-time microsimulation model. The model population was updated annually from 1970 to 2040 to account for births, deaths, net migration, and incident cases of childhood cancer. Prevalent individuals were followed until death, emigration, or the last year of simulation. Median population-based outcomes with 95% credible intervals (CrIs) were generated using Monte Carlo simulation. The methodology to derive model inputs included generalized additive modeling of cancer incidence, parametric survival modeling, and stochastic population forecasting. Individual-level data from provincial cancer registries for years 1970 to 2019 informed cancer-related model inputs and internal validation. The number of children (aged 0-14 y) diagnosed with cancer in Ontario is projected to rise from 414 (95% CrI: 353-486) in 2020 to 561 (95% CrI: 481-653) in 2039. The 5-y overall survival rate for 2030-2034 is estimated to reach 90% (95% CrI: 88%-92%). By 2040, 24,088 (95% CrI: 22,764-25,648) individuals with a history of childhood cancer (diagnosed in Ontario or elsewhere) are projected to reside in the province. The model accurately reproduced historical trends in incidence, survival, and prevalence when validated. The rising incidence and prevalence of childhood cancer will create increased demand for both acute cancer care and long-term follow-up services in Ontario. The POSIM-Prev model can be used to support long-range health system planning and future health technology assessments in jurisdictions that have access to similar model inputs. This article describes the development of a population-based, discrete-time microsimulation model that can simulate incident and prevalent cases of childhood cancer in Ontario, Canada, until 2040.Use of an open cohort framework allowed for estimation of the potential impact of net migration on childhood cancer prevalence.In addition to supporting long-term health system planning, this model can be used in future health technology assessments, by providing a demographic profile of incident and prevalent cases for model conceptualization and budget impact purposes.This modeling framework is adaptable to other jurisdictions and disease areas where individual-level data for incidence and survival are available.

An Investigation of the Discrete-Time Model Subject to Immigration, Harvesting, and Allee Effect

This paper deals with the dynamic behaviors of a discrete-time fractional-order predator–prey model in the presence of both the Allee effect and immigration on the prey population and in the presence of harvesting on the predator population. The existence and uniqueness and parametric conditions for local asymptotic stability of fixed points of the discrete-time fractional-order model are studied. Moreover, using the center manifold theorem and bifurcation theory, it is shown that the considered model undergoes flip and Neimark–Sacker bifurcations in a small neighborhood of the interior fixed point. Then, the direction of bifurcation is calculated. A feedback controller is implemented in the proposed model to control chaos thanks to the emergence of the Neimark–Sacker bifurcation. Furthermore, numerical analysis confirms the theoretical analysis with the help of Matlab software.

Income inequality and access to advanced immunotherapy for lung cancer: the case of Durvalumab in the Netherlands.

With the introduction of immunotherapy with non-small lung cancer, prognosis of these patients has improved. However, socio-economic differences in access to various immunotherapy treatments have been reported. In the Netherlands, such differences are not expected due to universal insurance coverage. We investigated the existence of differential susceptibility by socioeconomic status (SES) of the effect of distance to treatment hospital on access to Durvalumab in patients with stage III non-small lung cancer who received chemoradiation, and the influence of differential mortality. We used data from the Netherlands Cancer Registry (n = 3774) from the period 2017-2021. First, we fitted Bayesian discrete failure time models and compared SES-by-distance-to-hospital interaction to a baseline model including age, distance, SES and performance score. We then fitted a time to mortality model and used both models in a g-formula to simulate a scenario where mortality levels were equalized. Our results showed that the high SES group received Durvalumab more often than the low SES group (HR = 1.23, CI95% = [1.07, 1.53]), and even 4 kilometer distance increase leads to less Durvalumab (HR = 0.93, CI95% = [0.86, 0.99]). Bayes factor < 3 indicated inconclusive evidence for a SES by distance interaction effect, while g-formula results showed that differential mortality does not affect SES differences. Secondary analyses showed strong evidence that SES differences in using Durvalumab were constant over the years (Bayes factor > 17). Overall, these results are significant for understanding how socio-economic inequality affects proper care and can be vital for public policy.

Poor Olfaction and Risk of Stroke in Older Adults: The Atherosclerosis Risk in Communities Study.

Poor olfaction may be associated with adverse cerebrovascular events, but empirical evidence is limited. We aimed to investigate the association of olfaction with the risk of stroke in the Atherosclerosis Risk in Communities Study. We included 5799 older adults with no history of stroke at baseline from 2011 to 2013 (75.5±5.1 years, 59.0% female and 22.2% Black). Olfaction was assessed by the 12-item Sniffin' Sticks odor identification test and defined as poor (number correct ≤8), moderate (9-10), or good (11-12). Participants were followed from baseline to the date of the first stroke, death, last contact, or December 31, 2020, whichever occurred first. We used the discrete-time subdistribution hazard model to estimate the marginal cumulative incidence of stroke across olfactory statuses and adjusted risk ratios, accounting for covariates and competing risk of death. After up to 9.6 years of follow-up, we identified 332 incident stroke events. The adjusted marginal cumulative incidence of stroke at 9.6-year follow-up was 5.3% (95% CI, 4.2%-6.3%), 5.9% (95% CI, 4.8%-7.1%), and 7.7% (95% CI, 6.5%-9.1%) for good, moderate, and poor olfaction, respectively. Compared with good olfaction, poor olfaction was significantly associated with higher stroke risk throughout follow-up, albeit the association modestly attenuated after 6 years. Specifically, the adjusted risk ratios were 2.14 (95% CI, 1.22-3.94) at year 2, 1.98 (95% CI, 1.43-3.02) at year 4, 1.91 (95% CI, 1.43-2.77) at year 6, 1.49 (95% CI, 1.17-2.00) at year 8, and 1.45 (95% CI, 1.16-1.95) at year 9.6. Results were robust in multiple subgroup and sensitivity analyses. In older adults, poor olfaction assessed by a single olfaction test was associated with the higher risk of stroke in the next 10 years.

Exploring complex dynamics in a Ricker type predator-prey model with prey refuge.

This study examines the complexities of a discrete-time predator-prey model by integrating the impact of prey refuge, with the goal of providing a more realistic understanding of predator-prey interactions. We explore the existence and stability of fixed points within the model, offering a thorough examination of these critical aspects. Furthermore, we use center manifold and bifurcation theory to thoroughly analyze the presence and direction of period-doubling and Neimark-Sacker bifurcations. We also provide numerical simulations to validate our theoretical findings and demonstrate the intricacy of the model. The findings suggest that the inclusion of prey refuge has a notable stabilizing impact on the predator-prey model, hence enhancing the overall stability and resilience of the ecosystem.

Gradient test to assess homogeneity of probabilities in discrete-time transition models with application in agricultural science data

Longitudinal studies in discrete or continuous time involving categorical data are common in agricultural sciences. Transition models can be used as a means to analyse the resulting data, especially when the aim is to describe category changes over time, as well as to accommodate covariates due to experimental design. Here we focus on discrete-time models, for which it is critical to assess whether the underlying process is stationary or not. Tests based on likelihood procedures are very useful, and here we propose the Gradient test to assess stationary, or homogeneity of transition probabilities. We carried out simulation studies to evaluate the performance of the proposed test, which indicated a good performance regarding type-I error and power when compared to other classical tests available in the literature. As motivation we present two studies with agricultural data, the first one applied to entomology with nominal responses and the second application refers to the degree of injury in pigs. Using our proposed test, stationarity and non-stationarity were verified respectively in the applications. Since the gradient test to assess stationarity has a simplified structure when compared to other tests, it is therefore a useful alternative when carrying out inference in these types of models.

Parent-Adult Child Relationships and Repartnering After Gray Divorce.

The rise in gray divorce has catalyzed repartnering in later life. However, the antecedents of older adult repartnering remain poorly understood, particularly the potential role of adult children. A form of ambiguous loss, marital disruption often leads to family boundary ambiguity, thereby weakening family ties. We investigated whether co-residence and proximity of, frequent contact with, and downward transfers to adult children were negatively associated with repartnering after gray divorce. Data from the 1998-2018 Health and Retirement Study were used to estimate discrete-time event history models using logistic regression to predict repartnering after gray divorce among parents of adult children (N = 1,359). As expected, adult child co-residence as well as having a child who lived nearby and had frequent contact diminished the likelihood of repartnering. Parents whose children either did not live nearby or were nearby but did not have frequent contact were more likely to repartner than those with children nearby and in frequent contact or co-residing, signaling that both proximity and frequency of contact are related to repartnering. Additionally, the provision of financial support to adult children was associated with a lower risk of repartnering. Relationships with adult children shape parental repartnering behaviors. Echoing the concept of boundary ambiguity, our findings indicate that stronger family ties, as signaled by child co-residence or proximity and frequent contact as well as economic provision, tend to deter repartnering. These findings also indicate that absent strong family ties, older adults are more likely to form a new union.

Performance and Energy Consumption Analysis for UWSNs with Priority Scheduling Based on Access Probability and Wakeup Threshold.

As advancements in autonomous underwater vehicle (AUV) technology unfold, the role of underwater wireless sensor networks (UWSNs) is becoming increasingly pivotal. However, the high energy consumption in these networks can significantly reduce their operational lifespan, while latency issues can impair overall network performance. To address these challenges, a novel mixed packet forwarding strategy is developed, which incorporates a wakeup threshold and a dynamically adjusted access probability for the cluster head (CH). This approach aims to conserve energy while maintaining acceptable network latency levels. The wakeup threshold restricts the frequency of state switching for the CH, thereby reducing energy consumption. Meanwhile, the dynamic access probability regulates the influx of packets to mitigate system congestion based on current network conditions. Furthermore, to accommodate the network's varied transmission demands, packets generated by sensor nodes (SNs) are categorized into two types according to their sensitivity to latency. A discrete-time queueing model with preemptive priority is then established to evaluate the performance of different packets and the CH. Numerical results show how different parameters affect network performance and demonstrate that the proposed mixed packet forwarding mechanism can effectively manage the trade-off between latency and energy consumption, outperforming the traditional mechanism within a specific range of parameters.

Local dynamic analysis of the covid-19 mathematical model based on discrete-time predator-prey population model

Local dynamic analysis of the covid-19 mathematical model based on discrete-time predator-prey population model

Modeling the Mutation and Competition of Certain Nutrient-Producing Protocells by Means of Specific Turing Machines

Abstract It is very important to model the behavior of protocells as basic lifelike artificial organisms more and more accurately from the level of genomes to the level of populations. A better understanding of basic protocell communities may help us in describing more complex ecological systems accurately. In this article, we propose a new comprehensive, bilevel mathematical model of a community of three protocell species (one generalist and two specialists). The aim is to achieve a model that is as basic/fundamental as possible while already displaying mutation, selection, and complex population dynamics phenomena (like competitive exclusion and keystone species). At the microlevel of genetic codes, the protocells and their mutations are modeled with Turing machines (TMs). The specialists arise from the generalist by means of mutation. Then the species are put into a common habitat, where, at the macrolevel of populations, they have to compete for the available nutrients, a part of which they themselves can produce. Because of different kinds of mutations, the running times of the species as TMs (algorithms) are different. This feature is passed on to the macrolevel as different reproduction times. At the macrolevel, a discrete-time dynamic model describes the competition. The model displays complex lifelike behavior known from population ecology, including the so-called competitive exclusion principle and the effect of keystone species. In future works, the bilevel model will have a good chance of serving as a simple and useful tool for studying more lifelike phenomena (like evolution) in their pure/abstract form.

The Stability of the Global Wheat Trade in the Post-Soviet Space: A Trade Duration Approach

The collapse of the Soviet Union and the Iron Wall as well as the emergence of Kazakhstan, Russia, Ukraine and Romania as major actors on international grain markets since 2000 had increased the hope for a more stable international grain market. However, various short-run trade policy interventions of post-Soviet grain exporting countries during the 2000s and 2010s have caused temporary disruptions in global grain supply chains. Moreover, the growing number of protectionist state interventions and sanctions since the beginning of the 2010s, as well as growing geopolitical tensions, may also fragment global trade and thus threaten the stability of grain trade relations. Against this backdrop and given the current public and political debates about suitable “de-risking strategies” to stabilise international trade, this article aims to explore the stability of the global wheat trade in terms of the duration dependence of trade relations between the major grain exporters and their destinations from 2001 to 2021. We test whether there are differences between the relatively “new” post-Soviet exporters that have emerged and the “old” ones. Furthermore, we examine the correlation between the number of trade partners and the trade duration. We employ a discrete-time hazard model to annual trade data to estimate the baseline hazard and survival rate for eleven major wheat exporting countries. The results indicate that, by having overall duration dependence, no different pattern in trade stability can be identified between “new” and “old” actors, and initial indications suggest that having more trading partners favours the survival of trade relations.

Networked Predictive Trajectory Tracking Control for Underactuated USV with Time-Varying Delays

This study explores the control framework for the trajectory tracking problem concerning unmanned surface vessels (USVs) in the presence of time-varying communication delays. To address the aforementioned problem, a novel networked predictive sliding mode control architecture is proposed by integrating a discrete sliding mode control technique and predictive control scheme. By leveraging a first-order forward Euler discretization approach, a discrete-time model of USVs was initially formulated. Then, a virtual velocity controller was developed to convert the position tracking into expected velocity tracking, which was achieved by utilizing a sliding mode control. Subsequently, a networked predictive control technique was performed to compensate for the time-varying delays. Finally, theoretical analysis and extensive comparative simulation tests demonstrated that the proposed control scheme guaranteed complete compensation for time-varying delays while ensuring the stability of the closed-loop system.

Discrete-time host-parasitoid model incorporating dynamic regulatory factor for integrated control measures

In the realm of integrated pest management (IPM), the intensity of IPM should be dynamically adjusted over time according to pests in practical applications. To address this, we involve a dynamic regulatory factor of the IPM into the discrete model rather than switching system. Further, the existence and local stability of the fixed points and interesting bifurcation diagrams have been analysed and provided. Numerical investigations validate the theoretical results and reveal a diverse and intricate dynamical behaviour of the proposed system, which can be confirmed by a more detailed bifurcation analyses at the economic threshold level as the regulatory factors and intensity of IPM vary. The results illustrate that adjusting the intensity of IPM not only maintain the density of host at the threshold level, but also lead to an increase in parasitoid. The modelling methods and main results developed here provide valuable insights for formulating optimal control strategies.

How a responsive reproduction factor is determinant in a prey-predator dynamics: A numerical and analytical study in a discrete-time model.

In this work, we investigate the dynamics of a discrete-time prey-predator model considering a prey reproductive response as a function of the predation risk, with the prey population growth factor governed by two parameters. The system can evolve toward scenarios of mutual or only of predators extinction, or species coexistence. We analytically show all different types of equilibrium points depending on the ranges of growth parameters. By numerical study, we find the occurrence of quasiperiodic, chaotic, and hyperchaotic behaviors. Our analytical results are corroborated by the numerical ones. We highlight Arnold tongue-like periodic structures organized according to the Farey sequence, as well as pairs of twin shrimps connected by two links. The mathematical model captures two possible prey responsive strategies, decreasing or increasing the reproduction rate under predatory threat. Our results support that both strategies are compatible with the populations coexistence and present rich dynamics.

In search of lost time: Discrete- versus continuous-time models of working alliance and symptom severity.

The therapeutic alliance is one of the most stable predictors of symptom burden over the course of therapy. So far, this effect has only been examined on the basis of sessions. Continuous-time models (CTM) allow this relationship to be modeled as a continuous process in which the actual time interval between measurements is considered. The aim of the present study was to compare the fit of discrete-time models (DTM) of the alliance-symptom relationship with CTM using different time variables (sessions vs. actual time interval). Data from 1,413 patients at a university psychotherapy outpatient clinic were analyzed. The alliance and symptom burden were assessed each session with the Bernese Session Report and the Hopkins Symptom Checklist-Short-Form, respectively. Different DTM and CTM were estimated using the R-package ctsem and compared in their fit via the Akaike information criterion. CTMs with session as the time unit fitted the data best. Significant negative within-person effects of alliance and symptom burden were found. These effects showed a significant positive correlation, implying that individuals with a stronger effect of the alliance on symptom severity also showed a stronger effect of symptom severity on the alliance. When modeling the relationship of symptom severity and alliance, it seems to be of more importance to capture the fact that a session occurred than to capture the exact time intervals between sessions. Future studies should examine this finding for other psychotherapeutic factors. Interpersonal factors might explain the positive association of the reciprocal alliance-symptom effects. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

A generalized projection estimation algorithm

Given a linear regression model in discrete-time containing a vector of p constant uncertain parameters, this paper addresses the problem of designing an exponentially convergent parameter estimation algorithm, even when the regressor vector is not persistently exciting (not even in a finite time interval). On the basis of the definition of lack of persistency of excitation of order q for the regressor vector, 0≤q≤p (which coincides with the classical definition of persistency of excitation when q=0), a generalized projection estimation algorithm is proposed which guarantees global exponential convergence of the parameter estimation error and allows for the on-line computation of the order q of the lack of persistency of excitation. When the lack of persistency of excitation is of order zero, global exponential convergence to zero of the parameter estimation error is obtained, recovering a well-known result and the projection estimation algorithm as a special case.

Qualitative study for the system of waste plastic management in the ocean: A discrete-time deterministic model

Qualitative study for the system of waste plastic management in the ocean: A discrete-time deterministic model

Prediction of pavement friction using Markov chain at the project and network levels

ABSTRACT Pavement friction studies continue to focus on reducing wet-weather accidents as lack of friction or skid resistance has been linked to a portion of those vehicle accidents on wet pavements. Probabilistic models for predicting pavement friction or skid resistance as a function of surface age, at both the project and the network levels, are presented. The models deploy the discrete-time Markov model to predict the deterioration of both asphalt (AC) and concrete (PC) pavements. A pavement management system can utilise such predictive models for monitoring and rehabilitation of segments with marginal pavement friction. Two case studies are presented to demonstrate the potential uses of the proposed models. A non-homogeneous Markov chain was used to predict the future friction number (FN) for 12 sample projects using an analysis period of up to 10-year with the estimation error being less than (0.001). On the other hand, a homogeneous chain was employed to estimate the future state probabilities for both AC and PC sample networks using a 5-year analysis period, resulting in high correlations between observed and estimated state probabilities. Data used in the studies were obtained from the Long-Term Pavement Performance Program (LTPP) database. The data was treated such that AC friction records were corrected for testing temperature variations and friction data was sorted by type of test tyre used.

The 2 -burning Number of a Graph

We study a discrete-time model for the spread of information in a graph, motivated by the idea that people believe a story when they learn of it from two different origins. Similar to the burning number, in this problem, information spreads in rounds and a new source can appear in each round. For a graph , we are interested in , the minimum number of rounds until the information has spread to all vertices of graph . We are also interested in finding , the minimum number of sources necessary so that the information spreads to all vertices of in rounds. In addition to general results, we find and for the classes of spiders and wheels and show that their behavior differs with respect to these two parameters. We also provide examples and prove upper bounds for these parameters for Cartesian products of graphs.

Are current follow-up intervals justified in patients with non-emergent aortic surgeries?

Evidence for different surveillance protocols following aortic treatment is still lacking. Aim of this study was to analyze the clinical relevance of a first follow-up visit after 6 months. Between 01/2018 and 12/2019, 464 patients treated for non-emergent aortic pathologies were retrospectively analysed. Incidence of aortic events during follow-up (ie death, reintervention, endoleaks, anastomotic/new aneurysms, and diameter progression over time) was investigated. A discrete-time non-homogeneous Markov-chain model was used to analyse the data and to arrive at the number of skipped 6-month follow-up visits needed to harm a patient. After 6 months 2 (1.77%) patients had died, 15 (15.31%) patients suffered from aortic events, and a total of 4 (3.67%) patients had undergone reintervention after endovascular surgery, compared to 0 deaths, 2 (0.59%) patients with aortic events and 5 (1.48%) reinterventions after open-surgery. In our Markov Chain Model, after 6 months, 4.75% of patients showed aortic events, received a reintervention, or died. Sixty patients would need to skip their 6-month follow-up visit for one indication for reintervention to go unnoticed. Only 24 would need to skip it for one complication to go by unnoticed. This number is 55 after open surgery and 9 after endovascular. After elective endovascular or open aortic surgery without immediate in-hospital postoperative aortic events, the first follow-up visit after 6 months is important. Extending the first interval to longer time periods might lead to a considerable increase in missed aortic events. The cost and radiation exposure of frequent follow-ups must be balanced against the benefits of early preventative aortic interventions, warranting further research.