In this work, we develop a data-driven modelling framework to reproduce the locomotion of fish in a confined environment. Specifically, we highlight the primary characteristics of the motion of individual zebrafish (Danio rerio), and study how these can be suitably encapsulated within a mathematical framework utilising a limited number of calibrated model parameters. Using data captured from individual zebrafish via automated visual tracking, we develop a model using stochastic differential equations and describe fish as a self propelled particle moving in a plane. Based on recent experimental evidence of the importance of speed regulation in social behaviour, we extend stochastic models of fish locomotion by introducing experimentally-derived processes describing dynamic speed regulation. Salient metrics are defined which are then used to calibrate key parameters of coupled stochastic differential equations, describing both speed and angular speed of swimming fish. The effects of external constraints are also included, based on experimentally observed responses. Understanding the spontaneous dynamics of zebrafish using a bottom-up, purely data-driven approach is expected to yield a modelling framework for quantitative investigation of individual behaviour in the presence of various external constraints or biological assays.Electronic supplementary materialThe online version of this article (doi:10.1007/s00285-014-0843-2) contains supplementary material, which is available to authorized users.

Zebrafish are rapidly emerging as a powerful model organism in hypothesis-driven studies targeting a number of functional and dysfunctional processes. Mathematical models of zebrafish behaviour can inform the design of experiments, through the unprecedented ability to perform pilot trials on a computer. At the same time, in-silico experiments could help refining the analysis of real data, by enabling the systematic investigation of key neurobehavioural factors. Here, we establish a data-driven model of zebrafish social interaction. Specifically, we derive a set of interaction rules to capture the primary response mechanisms which have been observed experimentally. Contrary to previous studies, we include dynamic speed regulation in addition to turning responses, which together provide attractive, repulsive and alignment interactions between individuals. The resulting multi-agent model provides a novel, bottom-up framework to describe both the spontaneous motion and individual-level interaction dynamics of zebrafish, inferred directly from experimental observations.

Abstract. Models of collective animal motion can greatly aid in the design and interpretation of behavioural experiments that seek to unravel, isolate, and manipulate the determinants of leader-follower relationships. Here, we develop an initial model of zebrafish social behaviour, which accounts for both speed and angular velocity regulatory interactions among conspecifics. Using this model, we analyse the macroscopic observables of small shoals influenced by an "informed" agent, showing that leaders which actively modulate their speed with respect to their neighbours can entrain and stabilise collective dynamics of the naïve shoal.

BackgroundRegular testing for sexually transmitted infections (STIs) is important to maintain sexual health. Self-sampling kits ordered online and delivered in the post may increase access, convenience, and cost-effectiveness. Sexual health economies may target limited resources more effectively by signposting users toward Web-based or face-to-face services according to clinical need.ObjectiveThe aim of this paper was to investigate the impact of two interventions on testing activity across a whole sexual health economy: (1) the introduction of open access Web-based STI testing services and (2) a clinic policy of triage and signpost online where users without symptoms who attended clinics for STI testing were supported to access the Web-based service instead.MethodsData on attendances at all specialist public sexual health providers in an inner-London area were collated into a single database. Each record included information on user demographics, service type accessed, and clinical activity provided, including test results. Clinical activity was categorized as a simple STI test (could be done in a clinic or online), a complex visit (requiring face-to-face consultation), or other.ResultsIntroduction of Web-based services increased total testing activity across the whole sexual health economy by 18.47% (from 36,373 to 43,091 in the same 6-month period—2014-2015 and 2015-2016), suggesting unmet need for testing in the area. Triage and signposting shifted activity out of the clinic onto the Web-based service, with simple STI testing in the clinic decreasing from 16.90% (920/5443) to 12.25% (511/4172) of total activity, P<.001, and complex activity in the clinic increasing from 69.15% (3764/5443) to 74.86% (3123/4172) of total activity, P<.001. This intervention created a new population of online users with different demographic and clinical profiles from those who use Web-based services spontaneously. Some triage and signposted users (29.62%, 375/1266) did not complete the Web-based testing process, suggesting the potential for missed diagnoses.ConclusionsThis evaluation shows that users can effectively be transitioned from face-to-face to Web-based services and that this introduces a new population to Web-based service use and changes the focus of clinic-based activity. Further development is underway to optimize the triage and signposting process to support test completion.

Background Online testing for sexually transmitted infections has a lower unit cost than testing in clinical services and economic analysis has focused on the cost per test and cost per diagnosis in clinics and online. However, online services generate new demand for testing and shift activity between services, requiring system-level analysis to effectively predict cost-effectiveness. Methods and findings Routinely collected, anonymised, retrospective data on sexual health service activity from all specialist services (clinic and online) within an inner London sexual health economy were collated and harmonised to generate a complete dataset of individual level clinic attendances. Clinic activity and diagnoses were coded using nationally standardised codes assigned by clinicians. Costs were taken from locally or regionally agreed sexual health tariffs. The introduction of online services changed patterns of testing . In an inner London sexual health economy , online STI testing increased total number of tests , the total cost of testing and total diagnoses while slightly reducing the average cost per diagnosis . Two years after the introduction of online services 37% of tests in the were provided online and total diagnoses increased . The positivity of online services is generally lower than that in clinics but varies between contexts. Where the positivity ratio between clinic and online is less than the cost ratio, online services will reduce cost per diagnosis. In this analysis, areas with different classifications as urban and rural had different clinic/online positivity ratios changing the cost effectiveness between areas. Even after the introduction of online services, simple STI testing activity continues in clinics and providers should consider online-first options where clinically appropriate. Conclusions Online services for STI testing are not ‘stand alone’. They change STI testing behaviour with impacts on all elements of the sexual health economy. Planning, development and monitoring of such services should reference the dynamic nature of these systems and the role of online services within them.