Math

  • Modeling methodology

    Mathematical models are invaluable for exploring the dynamics of infectious diseases, health delivery systems, intervention strategies, and other public health concerns. With technological advancements and the progression of AI, models are more accessible than ever before. However, it can be difficult to balance model selection, performance, and usability. IDM’s modeling methodology teams are working to…

  • Estimating the Impact of Vaccination Campaigns on Measles Transmission in Somalia

    Somalia is a complex and fragile setting with a demonstrated potential for disruptive, high-burden measles outbreaks. In response, since 2018, Somalian authorities have partnered with UNICEF and the WHO to implement measles vaccination campaigns across the country. In this paper, we create a Somalia-specific model of measles transmission based on a comprehensive epidemiological dataset including…

  • A modeling approach for estimating dynamic measles case detection rates

    The main idea in this paper is that the age associated with reported measles cases can be used to estimate the number of undetected measles infections. Somewhat surprisingly, even with age only to the nearest year, estimates of underreporting can be generated at the much faster, 2 week time-scale associated with measles transmission. I describe…

  • Changes in on-time vaccination following the introduction of an electronic immunization registry, Tanzania 2016-2018: interrupted time-series analysis

    Background Digital health interventions (DHI) have the potential to improve the management and utilization of health information to optimize health care worker performance and provision of care. Despite the proliferation of DHI projects in low-and middle-income countries, few have been evaluated in an effort to understand their impact on health systems and health-related outcomes. Although…

  • Beyond R0: Heterogeneity in secondary infections and probabilistic epidemic forecasting

    The basic reproductive number, R0, is one of the most common and most commonly misapplied numbers in public health. Often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that different epidemics can exhibit, even when they have the same R0. Here, we reformulate and extend a classic result from…

  • Application of a Second-order Stochastic Optimization Algorithm for Fitting Stochastic Epidemiological Models

    Epidemiological models have tremendous potential to forecast disease burden and quantify the impact of interventions. Detailed models are increasingly popular, however these models tend to be stochastic and very costly to evaluate. Fortunately, readily available high-performance cloud computing now means that these models can be evaluated many times in parallel. Here, we briefly describe PSPO,…

  • Analysis of vaccination campaign effectiveness and population immunity to support and sustain polio elimination in Nigeria

    Background The world is closer than ever to a polio-free Africa. In this end-stage, it is important to ensure high levels of population immunity to prevent polio outbreaks. Here, we introduce a new method of assessing vaccination campaign effectiveness and estimating immunity at the district-level. We demonstrate how this approach can be used to plan…

  • Extracting transmission networks from phylogeographic data for epidemic and endemic diseases: Ebola virus in Sierra Leone, 2009 H1N1 pandemic influenza and polio in Nigeria

    Background Phylogeography improves our understanding of spatial epidemiology. However, application to practical problems requires choices among computational tools to balance statistical rigor, computational complexity, sensitivity to sampling strategy and interpretability. Methods We introduce a fast, heuristic algorithm to reconstruct partially-observed transmission networks (POTN) that combines features of phylogenetic and transmission tree approaches. We compare the…

  • Stochastic parameter search for events

    Background With recent increase in affordability and accessibility of high-performance computing (HPC), the use of large stochastic models has become increasingly popular for its ability to accurately mimic the behavior of the represented biochemical system. One important application of such models is to predict parameter configurations that yield an event of scientific significance. Due to…

  • Fun with Maths: Exploring Implications of Mathematical Models for Malaria Eradication

    Mathematical analyses and modelling have an important role informing malaria eradication strategies. Simple mathematical approaches can answer many questions, but it is important to investigate their assumptions and to test whether simple assumptions affect the results. In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of…