A Mathematical Framework for Agent Based Models of Complex Biological Networks

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis.Comment: To appear in Bulletin of Mathematical Biolog

The global retinoblastoma outcome study : a prospective, cluster-based analysis of 4064 patients from 149 countries

DATA SHARING : The study data will become available online once all analyses are complete.BACKGROUND : Retinoblastoma is the most common intraocular cancer worldwide. There is some evidence to suggest that major differences exist in treatment outcomes for children with retinoblastoma from different regions, but these differences have not been assessed on a global scale. We aimed to report 3-year outcomes for children with retinoblastoma globally and to investigate factors associated with survival. METHODS : We did a prospective cluster-based analysis of treatment-naive patients with retinoblastoma who were diagnosed between Jan 1, 2017, and Dec 31, 2017, then treated and followed up for 3 years. Patients were recruited from 260 specialised treatment centres worldwide. Data were obtained from participating centres on primary and additional treatments, duration of follow-up, metastasis, eye globe salvage, and survival outcome. We analysed time to death and time to enucleation with Cox regression models. FINDINGS : The cohort included 4064 children from 149 countries. The median age at diagnosis was 23·2 months (IQR 11·0–36·5). Extraocular tumour spread (cT4 of the cTNMH classification) at diagnosis was reported in five (0·8%) of 636 children from high-income countries, 55 (5·4%) of 1027 children from upper-middle-income countries, 342 (19·7%) of 1738 children from lower-middle-income countries, and 196 (42·9%) of 457 children from low-income countries. Enucleation surgery was available for all children and intravenous chemotherapy was available for 4014 (98·8%) of 4064 children. The 3-year survival rate was 99·5% (95% CI 98·8–100·0) for children from high-income countries, 91·2% (89·5–93·0) for children from upper-middle-income countries, 80·3% (78·3–82·3) for children from lower-middle-income countries, and 57·3% (52·1-63·0) for children from low-income countries. On analysis, independent factors for worse survival were residence in low-income countries compared to high-income countries (hazard ratio 16·67; 95% CI 4·76–50·00), cT4 advanced tumour compared to cT1 (8·98; 4·44–18·18), and older age at diagnosis in children up to 3 years (1·38 per year; 1·23–1·56). For children aged 3–7 years, the mortality risk decreased slightly (p=0·0104 for the change in slope). INTERPRETATION : This study, estimated to include approximately half of all new retinoblastoma cases worldwide in 2017, shows profound inequity in survival of children depending on the national income level of their country of residence. In high-income countries, death from retinoblastoma is rare, whereas in low-income countries estimated 3-year survival is just over 50%. Although essential treatments are available in nearly all countries, early diagnosis and treatment in low-income countries are key to improving survival outcomes.The Queen Elizabeth Diamond Jubilee Trust and the Wellcome Trust.https://www.thelancet.com/journals/langlo/homeam2023Paediatrics and Child Healt

Sectoral patterns of firm exit in Italian provinces

Firm exit, Manufacturing, Services, Italian provinces, L60, L80, R12, R23,