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.

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.

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.