A novel queue-based stochastic epidemic model with adaptive stabilising control.

The main objective of this paper is to propose a novel SEIR stochastic epidemic model. A distinguishing feature of this new model is that it allows us to consider a setup under general latency and infectious period distributions. To some extent, queuing systems with infinitely many servers and a Markov chain with time-varying transition rate comprise the very technical underpinning of the paper. Although more general, the Markov chain is as tractable as previous models for exponentially distributed latency and infection periods. It is also significantly more straightforward and tractable than semi-Markov models with a similar level of generality. Based on stochastic stability, we derive a sufficient condition for a shrinking epidemic regarding the queuing system's occupation rate that drives the dynamics. Relying on this condition, we propose a class of ad-hoc stabilising mitigation strategies that seek to keep a balanced occupation rate after a prescribed mitigation-free period. We validate the approach in the light of the COVID-19 epidemic in England and in the state of Amazonas, Brazil, and assess the effect of different stabilising strategies in the latter setting. Results suggest that the proposed approach can curb the epidemic with various occupation rate levels if the mitigation is timely.

Modelling lung cancer diagnostic pathways using discrete event simulation.

The United Kingdom has one of the poorest lung cancer survival rates in Europe. In this study, to help design and evaluate a single lung cancer pathway (SCP) for Wales, existing diagnostic pathways and processes have been mapped and then modelled with a discrete event simulation. The validated models have been used to provide key performance indicators and to examine different diagnostic testing strategies. Under the current diagnostic pathways, the mean time to treatment was 72 days for surgery patients, 56 days for chemotherapy patients, and 61 days for radiotherapy patients. Our research demonstrated that by ensuring that the patient attends their first outpatient appointment within 7 days and streamlining the diagnostic tests would have the potential to remove approximately 11 days from the current lung cancer pathway resulting in a 21% increase in patients receiving treatment within the Welsh Government set target of 62 days.

Modelling and optimal control of multi strain epidemics, with application to COVID-19.

Reinfection and multiple viral strains are among the latest challenges in the current COVID-19 pandemic. In contrast, epidemic models often consider a single strain and perennial immunity. To bridge this gap, we present a new epidemic model that simultaneously considers multiple viral strains and reinfection due to waning immunity. The model is general, applies to any viral disease and includes an optimal control formulation to seek a trade-off between the societal and economic costs of mitigation. We validate the model, with and without mitigation, in the light of the COVID-19 epidemic in England and in the state of Amazonas, Brazil. The model can derive optimal mitigation strategies for any number of viral strains, whilst also evaluating the effect of distinct mitigation costs on the infection levels. The results show that relaxations in the mitigation measures cause a rapid increase in the number of cases, and therefore demand more restrictive measures in the future.

Factors influencing the delivery of cancer pathways: a summary of the literature.

PURPOSE: The study aims to summarise the literature on cancer care pathways at the diagnostic and treatment phases. The objectives are to find factors influencing the delivery of cancer care pathways; to highlight any interrelating factors; to find gaps in the literature concerning areas of research; to summarise the strategies and recommendations implemented in the studies. DESIGN/METHODOLOGY/APPROACH: The study used a qualitative approach and developed a causal loop diagram to summarise the current literature on cancer care pathways, from screening and diagnosis to treatment. A total of 46 papers was finally included in the analysis, which highlights the recurring themes in the literature. FINDINGS: The study highlights the myriad areas of research applied to cancer care pathways. Factors influencing the delivery of cancer care pathways were classified into different albeit interrelated themes. These include access barriers to care, hospital emergency admissions, fast track diagnostics, delay in diagnosis, waiting time to treatment and strategies to increase system efficiency. ORIGINALITY/VALUE: As far as the authors know, this is the first study to present a visual representation of the complex relationship between factors influencing the delivery of cancer care pathways.

Examining the diagnostic pathway for lung cancer patients in Wales using discrete event simulation.

BACKGROUND: UK's National Health Service (NHS) has one of the poorest lung cancer survival rates in Europe. To improve patient outcomes, a single cancer pathway was introduced in the NHS. In this study, a Discrete Event Simulation was developed to understand bottlenecks during lung cancer treatment. METHODS: This study focused on the lung cancer diagnostic pathways at two Welsh hospitals. Discrete Event Simulation is a computer-based method that has been effectively used in demand and capacity planning. In this study, simulation models were developed for the current and proposed single cancer pathways. The validated models were used to provide Key Performance Indicators. Several "what-if" scenarios were considered for the current and proposed pathways. RESULTS: Under the current diagnostic pathway, the mean time to treatment for a surgery patient was 68 days at the Royal Glamorgan Hospital and 79 days at Prince Charles Hospital. For chemotherapy patients, the mean time to treatment was 52 days at the Royal Glamorgan Hospital and 57 days at Prince Charles Hospital. For radiotherapy patients, the mean time to treatment was 44 days at Royal Glamorgan Hospital and 54 days at Prince Charles Hospital. Ensuring that the patient attends their first outpatient appointment within 7 days and streamlining the diagnostic tests would have the potential to remove approximately 20 days from the current lung cancer pathway resulting in a 20-25% increase of patients receiving treatment within 62 days. Ensuring that patients begin their treatment within 21 days of diagnosis sees almost all patients comply with the 62-day target. CONCLUSIONS: Discrete Event Simulation coupled with a detailed statistical analysis provides a useful decision support tool which can be used to examine the current and proposed lung cancer pathways in terms of time spent on the pathway.

Resource optimization for cancer pathways with aggregate diagnostic demand: a perishable inventory approach.

This work proposes a novel framework for planning the capacity of diagnostic tests in cancer pathways that considers the aggregate demand of referrals from multiple cancer specialties (sites). The framework includes an analytic tool that recursively assesses the overall daily demand for each diagnostic test and considers general distributions for both the incoming cancer referrals and the number of required specific tests for any given patient. By disaggregating the problem with respect to each diagnostic test, we are able to model the system as a perishable inventory problem that can be solved by means of generalized G/D/C queuing models, where the capacity [Formula: see text] is allowed to vary and can be seen as a random variable that is adjusted according to prescribed performance measures. The approach aims to provide public health and cancer services with recommendations to align capacity and demand for cancer diagnostic tests effectively and efficiently. Our case study illustrates the applicability of our methods on lung cancer referrals from UK's National Health Service.

Flattening the curves: on-off lock-down strategies for COVID-19 with an application to Brazil.

The current COVID-19 pandemic is affecting different countries in different ways. The assortment of reporting techniques alongside other issues, such as underreporting and budgetary constraints, makes predicting the spread and lethality of the virus a challenging task. This work attempts to gain a better understanding of how COVID-19 will affect one of the least studied countries, namely Brazil. Currently, several Brazilian states are in a state of lock-down. However, there is political pressure for this type of measures to be lifted. This work considers the impact that such a termination would have on how the virus evolves locally. This was done by extending the SEIR model with an on / off strategy. Given the simplicity of SEIR we also attempted to gain more insight by developing a neural regressor. We chose to employ features that current clinical studies have pinpointed has having a connection to the lethality of COVID-19. We discuss how this data can be processed in order to obtain a robust assessment. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s13362-020-00098-w.

Optimisation and control of the supply of blood bags in hemotherapic centres via Markov decision process with discounted arrival rate.

Running a cost-effective human blood transfusion supply chain challenges decision makers in blood services world-wide. In this paper, we develop a Markov decision process with the objective of minimising the overall costs of internal and external collections, storing, producing and disposing of blood bags, whilst explicitly considering the probability that a donated blog bag will perish before demanded. The model finds an optimal policy to collect additional bags based on the number of bags in stock rather than using information about the age of the oldest item. Using data from the literature, we validate our model and carry out a case study based on data from a large blood supplier in South America. The study helped achieve an overall increase of 4.5% in blood donations in one year.

Optimal testing policies for diagnosing patients with intermediary probability of disease.

This paper proposes a stochastic shortest path approach to find an optimal sequence of tests to confirm or discard a disease, for any prescribed optimality criterion. The idea is to select the best sequence in which to apply a series of available tests, with a view at reaching a diagnosis with minimum expenditure of resources. The proposed approach derives an optimal policy whereby the decision maker is provided with a test strategy for each a priori probability of disease, aiming to reach posterior probabilities that warrant either immediate treatment or a not-ill diagnosis.

Planning and understanding the intensive care network in the State of Rio de Janeiro (RJ), Brazil: a complex societal problem. / Planejamento e compreensão da rede de terapia intensiva no Estado do Rio de Janeiro: um problema social complexo.

OBJECTIVES: To determine the optimal number of adult intensive care unit beds to reduce patient's queue waiting time and to propose policy strategies. METHODS: Multimethodological approach: (a) quantitative time series and queueing theory were used to predict the demand and estimate intensive care unit beds in different scenarios; (b) qualitative focus group and content analysis were used to explore physicians' attitudes and provide insights into their behaviors and belief-driven healthcare delivery changes. RESULTS: A total of 33,101 requests for 268 regulated intensive care unit beds in one year resulted in 25% admissions, 55% queue abandonment and 20% deaths. Maintaining current intensive care unit arrival and exit rates, there would need 628 beds to ensure a maximum wait time of six hours. A reduction of the current abandonment rates due to clinical improvement or the average intensive care unit length of stay would decrease the number of beds to 471 and 366, respectively. If both were reduced, the number would reach 275 beds. The interviews generated 3 main themes: (1) the doctor's conflict: fair, legal, ethical and shared priorities in the decision-making process; (2) a failure of access: invisible queues and a lack of infrastructure; and (3) societal drama: deterioration of public policies and health care networks. CONCLUSION: The queue should be treated as a complex societal problem with a multifactorial origin requiring integrated solutions. Improving intensive care unit protocols and reengineering the general wards may decrease the length of stay. It is essential to redefine and consolidate the regulatory centers to organize the queue and provide available resources in a timely manner, by using priority criteria, working with stakeholders to guarantee clinical governance and network organization.

OBJETIVO: Determinar o número de leitos de UTI para pacientes adultos a fim de reduzir o tempo de espera na fila e propor políticas estratégicas. MÉTODOS: Abordagem multimetodológica: (a) quantitativa, através de séries temporais e teoria de filas, para prever a demanda e estimar o número de leitos de terapia intensiva em diferentes cenários; (b) qualitativa, através do grupo focal e análise do conteúdo, para explorar o comportamento, atitudes e as crenças dos médicos nas mudanças da saúde. RESULTADOS: As 33.101 solicitações de internação nos 268 leitos regulados de terapia intensiva, durante 1 ano, resultaram na admissão de 25% dos pacientes, 55% abandonos da fila e 20% de óbitos. Mantidas as taxas atuais de entrada e saída da unidade de terapia intensiva, seriam necessários 628 leitos para assegurar que o tempo máximo de espera fosse de 6 horas. A redução das atuais taxas de abandono, em razão de melhora clínica ou a redução do tempo médio de permanência na unidade, diminuiria o número de leitos necessários para 471 e para 366, respectivamente. Caso se conseguissem ambos os objetivos, o número chegaria a 275 leitos. As entrevistas geraram três temas principais: o conflito do médico: a necessidade de estabelecer prioridades justas, legais, éticas e compartilhadas na tomada de decisão; o fracasso no acesso: filas invisíveis e falta de infraestrutura; o drama social: deterioração das políticas públicas e desarticulação das redes de saúde. CONCLUSÃO: A fila deve ser tratada como um problema social complexo, de origem multifatorial e que requer soluções integradas. Redimensionar o número de leitos não é a única solução. Melhorar os protocolos e prover a reengenharia das enfermarias gerais podem reduzir o tempo de permanência na unidade. É essencial consolidar as centrais de regulação para organizar a fila e fornecer os recursos disponíveis em tempo adequado, usando critérios de prioridade e trabalhando em conjunto com as pessoas envolvidas para garantir a governança clínica e a organização da rede.

Planejamento e compreensão da rede de terapia intensiva no Estado do Rio de Janeiro: um problema social complexo / Planning and understanding the intensive care network in the State of Rio de Janeiro (RJ), Brazil: a complex societal problem

RESUMO Objetivo: Determinar o número de leitos de UTI para pacientes adultos a fim de reduzir o tempo de espera na fila e propor políticas estratégicas. Métodos: Abordagem multimetodológica: (a) quantitativa, através de séries temporais e teoria de filas, para prever a demanda e estimar o número de leitos de terapia intensiva em diferentes cenários; (b) qualitativa, através do grupo focal e análise do conteúdo, para explorar o comportamento, atitudes e as crenças dos médicos nas mudanças da saúde. Resultados: As 33.101 solicitações de internação nos 268 leitos regulados de terapia intensiva, durante 1 ano, resultaram na admissão de 25% dos pacientes, 55% abandonos da fila e 20% de óbitos. Mantidas as taxas atuais de entrada e saída da unidade de terapia intensiva, seriam necessários 628 leitos para assegurar que o tempo máximo de espera fosse de 6 horas. A redução das atuais taxas de abandono, em razão de melhora clínica ou a redução do tempo médio de permanência na unidade, diminuiria o número de leitos necessários para 471 e para 366, respectivamente. Caso se conseguissem ambos os objetivos, o número chegaria a 275 leitos. As entrevistas geraram três temas principais: o conflito do médico: a necessidade de estabelecer prioridades justas, legais, éticas e compartilhadas na tomada de decisão; o fracasso no acesso: filas invisíveis e falta de infraestrutura; o drama social: deterioração das políticas públicas e desarticulação das redes de saúde. Conclusão: A fila deve ser tratada como um problema social complexo, de origem multifatorial e que requer soluções integradas. Redimensionar o número de leitos não é a única solução. Melhorar os protocolos e prover a reengenharia das enfermarias gerais podem reduzir o tempo de permanência na unidade. É essencial consolidar as centrais de regulação para organizar a fila e fornecer os recursos disponíveis em tempo adequado, usando critérios de prioridade e trabalhando em conjunto com as pessoas envolvidas para garantir a governança clínica e a organização da rede.

ABSTRACT Objectives: To determine the optimal number of adult intensive care unit beds to reduce patient's queue waiting time and to propose policy strategies. Methods: Multimethodological approach: (a) quantitative time series and queueing theory were used to predict the demand and estimate intensive care unit beds in different scenarios; (b) qualitative focus group and content analysis were used to explore physicians' attitudes and provide insights into their behaviors and belief-driven healthcare delivery changes. Results: A total of 33,101 requests for 268 regulated intensive care unit beds in one year resulted in 25% admissions, 55% queue abandonment and 20% deaths. Maintaining current intensive care unit arrival and exit rates, there would need 628 beds to ensure a maximum wait time of six hours. A reduction of the current abandonment rates due to clinical improvement or the average intensive care unit length of stay would decrease the number of beds to 471 and 366, respectively. If both were reduced, the number would reach 275 beds. The interviews generated 3 main themes: (1) the doctor's conflict: fair, legal, ethical and shared priorities in the decision-making process; (2) a failure of access: invisible queues and a lack of infrastructure; and (3) societal drama: deterioration of public policies and health care networks. Conclusion: The queue should be treated as a complex societal problem with a multifactorial origin requiring integrated solutions. Improving intensive care unit protocols and reengineering the general wards may decrease the length of stay. It is essential to redefine and consolidate the regulatory centers to organize the queue and provide available resources in a timely manner, by using priority criteria, working with stakeholders to guarantee clinical governance and network organization.

Performance dos testes diagnósticos na probabilidade intermediária de doença coronariana: uma análise para auxílio à tomada de decisão / Performance of diagnostic tests for intermediate probabilities of coronary heart disease: a decision making analysis

Pacientes com probabilidade intermediária de doença coronariana são um desafio diagnóstico e é justamente nessa população onde o grau de incerteza é maior que os testes diagnósticos têm sua maior aplicabilidade. Entretanto, de acordo com a definição vigente, submeter uma população com probabilidade de doença entre 10 e 90% pode gerar exames desnecessários e resultados equivocados. Conhecer as características de cada teste, assim como riscos e benefícios do tratamento medicamentoso para doença coronariana e conjugar essas informações através dos limiares de diagnóstico trazem uma nova perspectiva à tomada de decisão. Revisar a origem dos conceitos atualmente preconizados de probabilidade intermediária e determinar os limiares de diagnóstico e tratamento dos testes não invasivos e, com base neles, propor um novo conceito de probabilidade intermediária de doença coronariana. Através da revisão bibliográfica foram extraídas metanálises nas quais dados de sensibilidade, especificidade, razão de verossimilhança positiva e negativa, riscos e benefícios dos testes e tratamento foram fornecidos. Utilizando-se algoritmo desenvolvido por Pauker e colaboradores foi possível obter os limiares de diagnóstico e tratamento ajustados para cada exame em questão. O conceito de probabilidade intermediária de doença coronariana é bastante amplo, variando, conforme os autores, entre 10 e 90%, 1 e 92%, 15 e 85%, com racionalidade distinta. Contemplando-se o poder discriminatório de cada exame, riscos dos testes, riscos e benefícios do tratamento, os limiares de diagnóstico e tratamento foram definidos para teste ergométrico (22-58%), eco-stress (10-72), cintilografia miocárdica (12-80%), ressonância nuclear magnética (16-80%) e angiotomografia de coronárias (6,7-81%). A decisão quanto à submissão aos testes diagnósticos deve ser individualizada, levando-se em consideração os limiares de diagnóstico e tratamento de cada método em questão

Difficulties in access and estimates of public beds in intensive care units in the state of Rio de Janeiro.

OBJECTIVE: To estimate the required number of public beds for adults in intensive care units in the state of Rio de Janeiro to meet the existing demand and compare results with recommendations by the Brazilian Ministry of Health. METHODS: The study uses a hybrid model combining time series and queuing theory to predict the demand and estimate the number of required beds. Four patient flow scenarios were considered according to bed requests, percentage of abandonments and average length of stay in intensive care unit beds. The results were plotted against Ministry of Health parameters. Data were obtained from the State Regulation Center from 2010 to 2011. RESULTS: There were 33,101 medical requests for 268 regulated intensive care unit beds in Rio de Janeiro. With an average length of stay in regulated ICUs of 11.3 days, there would be a need for 595 active beds to ensure system stability and 628 beds to ensure a maximum waiting time of six hours. Deducting current abandonment rates due to clinical improvement (25.8%), these figures fall to 441 and 417. With an average length of stay of 6.5 days, the number of required beds would be 342 and 366, respectively; deducting abandonment rates, 254 and 275. The Brazilian Ministry of Health establishes a parameter of 118 to 353 beds. Although the number of regulated beds is within the recommended range, an increase in beds of 122.0% is required to guarantee system stability and of 134.0% for a maximum waiting time of six hours. CONCLUSIONS: Adequate bed estimation must consider reasons for limited timely access and patient flow management in a scenario that associates prioritization of requests with the lowest average length of stay.

Difficulties in access and estimates of public beds in intensive care units in the state of Rio de Janeiro / Dificuldades de acesso e estimativas de leitos públicos para unidades de terapia intensiva no estado do Rio de Janeiro

ABSTRACT OBJECTIVE To estimate the required number of public beds for adults in intensive care units in the state of Rio de Janeiro to meet the existing demand and compare results with recommendations by the Brazilian Ministry of Health. METHODS The study uses a hybrid model combining time series and queuing theory to predict the demand and estimate the number of required beds. Four patient flow scenarios were considered according to bed requests, percentage of abandonments and average length of stay in intensive care unit beds. The results were plotted against Ministry of Health parameters. Data were obtained from the State Regulation Center from 2010 to 2011. RESULTS There were 33,101 medical requests for 268 regulated intensive care unit beds in Rio de Janeiro. With an average length of stay in regulated ICUs of 11.3 days, there would be a need for 595 active beds to ensure system stability and 628 beds to ensure a maximum waiting time of six hours. Deducting current abandonment rates due to clinical improvement (25.8%), these figures fall to 441 and 417. With an average length of stay of 6.5 days, the number of required beds would be 342 and 366, respectively; deducting abandonment rates, 254 and 275. The Brazilian Ministry of Health establishes a parameter of 118 to 353 beds. Although the number of regulated beds is within the recommended range, an increase in beds of 122.0% is required to guarantee system stability and of 134.0% for a maximum waiting time of six hours. CONCLUSIONS Adequate bed estimation must consider reasons for limited timely access and patient flow management in a scenario that associates prioritization of requests with the lowest average length of stay.

RESUMO OBJETIVO Determinar o número necessário de leitos públicos de unidades de terapia intensiva para adultos no estado do Rio de Janeiro para atender à demanda existente, e comparar os resultados com a recomendação do Ministério da Saúde. MÉTODOS Seguiu-se modelo híbrido que agrega séries temporais e teoria de filas para prever a demanda e estimar o número de leitos necessários. Foram considerados quatro cenários de fluxo de pacientes, de acordo com as solicitações de vagas, proporção de desistências e tempo médio de permanência no leito de unidade de terapia intensiva. Os resultados foram confrontados com os parâmetros do Ministério da Saúde. Os dados foram obtidos da Central Estadual de Regulação, de 2010 a 2011. RESULTADOS Houve 33.101 solicitações médicas para 268 leitos de unidade de terapia intensiva regulados no Rio de Janeiro. Com tempo médio de permanência das unidades de terapia intensiva reguladas de 11,3 dias, haveria necessidade de 595 leitos ativos para garantir a estabilidade do sistema e 628 leitos para o tempo máximo na fila de seis horas. Deduzidas as atuais taxas de desistência por melhora clínica (25,8%), estes números caem para 441 e 471. Com tempo médio de permanência de 6,5 dias, o número necessário seria de 342 e 366 leitos, respectivamente; deduzidas as taxas de desistência, de 254 e 275. O Ministério da Saúde estabelece parâmetro de 118 a 353 leitos. Embora o número de leitos regulados esteja na faixa recomendada, necessita-se incremento de 122,0% de leitos para garantir a estabilidade do sistema e de 134,0% para um tempo máximo de espera de seis horas. CONCLUSÕES O dimensionamento adequado de leitos deve considerar os motivos de limitações de acesso oportuno e a gestão do fluxo de pacientes em um cenário que associa priorização das solicitações com menor tempo médio de permanência.