Modeling Heterogeneity in Direct Infectious Disease Transmission in a Compartmental Model

Mathematical models have been used to understand the transmission dynamics of infectious diseases and to assess the impact of intervention strategies. Traditional mathematical models usually assume a homogeneous mixing in the population, which is rarely the case in reality. Here, we construct a new transmission function by using as the probability density function a negative binomial distribution, and we develop a compartmental model using it to model the heterogeneity of contact rates in the population. We explore the transmission dynamics of the developed model using numerical simulations with different parameter settings, which characterize different levels of heterogeneity. The results show that when the reproductive number, [GRAPHICS] , is larger than one, a low level of heterogeneity results in dynamics similar to those predicted by the homogeneous mixing model. As the level of heterogeneity increases, the dynamics become more different. As a test case, we calibrated the model with the case incidence data for severe acute respiratory syndrome (SARS) in Beijing in 2003, and the estimated parameters demonstrated the effectiveness of the control measures taken during that period

Fitting Early Phases of the COVID-19 Outbreak: A Comparison of the Performances of Used Models

The COVID-19 outbreak involved a spread of prediction efforts, especially in the early pandemic phase. A better understanding of the epidemiological implications of the different models seems crucial for tailoring prevention policies. This study aims to explore the concordance and discrepancies in outbreak prediction produced by models implemented and used in the first wave of the epidemic. To evaluate the performance of the model, an analysis was carried out on Italian pandemic data from February 24, 2020. The epidemic models were fitted to data collected at 20, 30, 40, 50, 60, 70, 80, 90, and 98 days (the entire time series). At each time step, we made predictions until May 31, 2020. The Mean Absolute Error (MAE) and the Mean Absolute Percentage Error (MAPE) were calculated. The GAM model is the most suitable parameterization for predicting the number of new cases; exponential or Poisson models help predict the cumulative number of cases. When the goal is to predict the epidemic peak, GAM, ARIMA, or Bayesian models are preferable. However, the prediction of the pandemic peak could be made carefully during the early stages of the epidemic because the forecast is affected by high uncertainty and may very likely produce the wrong results

Challenges for modelling interventions for future pandemics

Funding: This work was supported by the Isaac Newton Institute (EPSRC grant no. EP/R014604/1). MEK was supported by grants from The Netherlands Organisation for Health Research and Development (ZonMw), grant number 10430022010001, and grant number 91216062, and by the H2020 Project 101003480 (CORESMA). RNT was supported by the UKRI, grant number EP/V053507/1. GR was supported by Fundação para a Ciência e a Tecnologia (FCT) project reference 131_596787873. and by the VERDI project 101045989 funded by the European Union. LP and CO are funded by the Wellcome Trust and the Royal Society (grant 202562/Z/16/Z). LP is also supported by the UKRI through the JUNIPER modelling consortium (grant number MR/V038613/1) and by The Alan Turing Institute for Data Science and Artificial Intelligence. HBS is funded by the Wellcome Trust and Royal Society (202562/Z/16/Z), and the Alexander von Humboldt Foundation. DV had support from the National Council for Scientific and Technological Development of Brazil (CNPq - Refs. 441057/2020-9, 424141/2018-3, 309569/2019-2). FS is supported by the UKRI through the JUNIPER modelling consortium (grant number MR/V038613/1). EF is supported by UKRI (Medical Research Council)/Department of Health and Social Care (National Insitute of Health Research) MR/V028618/1. JPG's work was supported by funding from the UK Health Security Agency and the UK Department of Health and Social Care.Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross-disciplinary collaboration together with close communication between scientists and policy makers.Publisher PDFPeer reviewe

Statistical Approaches to Infectious Diseases Modelling in Developing Countries: A Case of COVID-19

Essential skills required for both statistical consulting and collaboration are mostly informal and are rarely taught in the training institutions in developing countries. These critical skills constitute a significant missing gap and a major hindrance to the growth and development of capacity in statistics and data science practice in developing countries. The advent of LISA 2020 initiative is bridging this gap with a fast-growing network of “stat labs” spread across higher education institutions in Africa, India, Brazil and other parts of the world. This chapter will highlight how LISA 2020 Stat Labs (and other potential labs outside LISA 2020) engage in building capacity to improve informal statistical skills through training and collaborations. In addition, the chapter will review the activities and programs of the stat labs and the contributions being made to bring data science to bear on real-world problems. The chapter plans to draw out lessons that are unique and common to the different stat labs in the network

The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study.

BACKGROUND: In December, 2019, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), a novel coronavirus, emerged in Wuhan, China. Since then, the city of Wuhan has taken unprecedented measures in response to the outbreak, including extended school and workplace closures. We aimed to estimate the effects of physical distancing measures on the progression of the COVID-19 epidemic, hoping to provide some insights for the rest of the world. METHODS: To examine how changes in population mixing have affected outbreak progression in Wuhan, we used synthetic location-specific contact patterns in Wuhan and adapted these in the presence of school closures, extended workplace closures, and a reduction in mixing in the general community. Using these matrices and the latest estimates of the epidemiological parameters of the Wuhan outbreak, we simulated the ongoing trajectory of an outbreak in Wuhan using an age-structured susceptible-exposed-infected-removed (SEIR) model for several physical distancing measures. We fitted the latest estimates of epidemic parameters from a transmission model to data on local and internationally exported cases from Wuhan in an age-structured epidemic framework and investigated the age distribution of cases. We also simulated lifting of the control measures by allowing people to return to work in a phased-in way and looked at the effects of returning to work at different stages of the underlying outbreak (at the beginning of March or April). FINDINGS: Our projections show that physical distancing measures were most effective if the staggered return to work was at the beginning of April; this reduced the median number of infections by more than 92% (IQR 66-97) and 24% (13-90) in mid-2020 and end-2020, respectively. There are benefits to sustaining these measures until April in terms of delaying and reducing the height of the peak, median epidemic size at end-2020, and affording health-care systems more time to expand and respond. However, the modelled effects of physical distancing measures vary by the duration of infectiousness and the role school children have in the epidemic. INTERPRETATION: Restrictions on activities in Wuhan, if maintained until April, would probably help to delay the epidemic peak. Our projections suggest that premature and sudden lifting of interventions could lead to an earlier secondary peak, which could be flattened by relaxing the interventions gradually. However, there are limitations to our analysis, including large uncertainties around estimates of R0 and the duration of infectiousness. FUNDING: Bill & Melinda Gates Foundation, National Institute for Health Research, Wellcome Trust, and Health Data Research UK