Critical slowing down near a bifurcation or limit point leads to a dynamical hysteresis that cannot be avoided by sweeping a control parameter slowly through the critical point. This paper analytically illustrates, with the help of a simple model, the bifurcation shift. We describe an inexpensive experiment using a semiconductor laser where this phenomenon occurs near the threshold of a semiconductor laser.

Respiratory disease trials are profoundly affected by non-pharmaceutical interventions (NPIs) against COVID-19 because they perturb existing regular patterns of all seasonal viral epidemics. To address trial design with such uncertainty, we developed an epidemiological model of respiratory tract infection (RTI) coupled to a mechanistic description of viral RTI episodes. We explored the impact of reduced viral transmission (mimicking NPIs) using a virtual population and in silico trials for the bacterial lysate OM-85 as prophylaxis for RTI. Ratio-based efficacy metrics are only impacted under strict lockdown whereas absolute benefit already is with intermediate NPIs (eg. mask-wearing). Consequently, despite NPI, trials may meet their relative efficacy endpoints (provided recruitment hurdles can be overcome) but are difficult to assess with respect to clinical relevance. These results advocate to report a variety of metrics for benefit assessment, to use adaptive trial design and adapted statistical analyses. They also question eligibility criteria misaligned with the actual disease burden.

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Clinical research in infectious respiratory diseases has been profoundly affected by non-pharmaceutical interventions (NPIs) against COVID-19. On top of trial delays or even discontinuation which have been observed in all disease areas, NPIs altered transmission pattern of many seasonal respiratory viruses which followed regular patterns for decades before the pandemic. Clinical trial design based on pre-pandemic historical data therefore needs to be put in question. In this article, we show how knowledge-based mathematical modeling can be used to address this issue. We set up an epidemiological model of respiratory tract infection (RTI) sensitive to a time dependent between-host transmission rate and coupled this model to a mechanistic description of viral RTI episodes in an individual patient. By reducing the transmission rate when the lockdown was introduced in the United Kingdom in March 2020, we were able to reproduce the perturbed 2020 RTI disease burden data. Using this setup, we simulated several NPIs scenarios of various strength (none, mild, medium, strong) and conducted placebo-controlled in silico clinical trials in pediatric patients with recurrent RTIs (RRTI) quantifying annual RTI rate distributions. In interventional arms, virtual patients aged 1-5 years received the bacterial lysate OM-85 (approved in several countries for the prevention of pediatric RRTIs) through a pro-type I immunomodulation mechanism of action described by a physiologically based pharmacokinetics and pharmacodynamics approach (PBPK/PD). Our predictions showed that sample size estimates based on the ratio of RTI rates (or the post-hoc power of fixed sample size trials) are not majorly impacted under NPIs which are less severe (none, mild and medium NPIs) than a strict lockdown (strong NPI). However, NPIs show a stronger impact on metrics more relevant for assessing the clinical relevance of the effect such as absolute benefit. This dichotomy shows the risk that successful trials (even with their primary endpoints being met) still get challenged in risk benefit assessment during the review of market authorization. Furthermore, we found that a mild NPI scenario already affected the time to recruit significantly when sticking to eligibility criteria complying with historical data. In summary, our model predictions can help rationalize and forecast post-COVID-19 trial feasibility. They advocate for gauging absolute and relative benefit metrics as well as clinical relevance for assessing efficacy hypotheses in trial design and they question eligibility criteria misaligned with the actual disease burden.