A practical guide to mathematical methods for estimating infectious disease outbreak risks

Mathematical models are increasingly used throughout infectious disease outbreaks to guide control measures. In this review article, we focus on the initial stages of an outbreak, when a pathogen has just been observed in a new location (e.g., a town, region or country). We provide a beginner's guide to two methods for estimating the risk that introduced cases lead to sustained local transmission (i.e., the probability of a major outbreak), as opposed to the outbreak fading out with only a small number of cases. We discuss how these simple methods can be extended for epidemiological models with any level of complexity, facilitating their wider use, and describe how estimates of the probability of a major outbreak can be used to guide pathogen surveillance and control strategies. We also give an overview of previous applications of these approaches. This guide is intended to help quantitative researchers develop their own epidemiological models and use them to estimate the risks associated with pathogens arriving in new host populations. The development of these models is crucial for future outbreak preparedness. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Global COVID-19 lockdown highlights humans as both threats and custodians of the environment

The global lockdown to mitigate COVID-19 pandemic health risks has altered human interactions with nature. Here, we report immediate impacts of changes in human activities on wildlife and environmental threats during the early lockdown months of 2020, based on 877 qualitative reports and 332 quantitative assessments from 89 different studies. Hundreds of reports of unusual species observations from around the world suggest that animals quickly responded to the reductions in human presence. However, negative effects of lockdown on conservation also emerged, as confinement resulted in some park officials being unable to perform conservation, restoration and enforcement tasks, resulting in local increases in illegal activities such as hunting. Overall, there is a complex mixture of positive and negative effects of the pandemic lockdown on nature, all of which have the potential to lead to cascading responses which in turn impact wildlife and nature conservation. While the net effect of the lockdown will need to be assessed over years as data becomes available and persistent effects emerge, immediate responses were detected across the world. Thus, initial qualitative and quantitative data arising from this serendipitous global quasi-experimental perturbation highlights the dual role that humans play in threatening and protecting species and ecosystems. Pathways to favorably tilt this delicate balance include reducing impacts and increasing conservation effectiveness.

Chronic stable angina: comparison of verapamil and propranolol

The effect of verapamil 120 mg t.d.s. was compared with propranolol 160 mg b.d. in the treatment of stable angina pectoris. Nineteen patients were studied in a randomized, double-blind, crossover trial, using patient diaries, exercise-testing and ambulatory electrocardiographic monitoring. Both drugs were given for 1 month. On average the number of attacks of angina was reduced equally by verapamil and propranolol. The degree of electrocardiographic evidence of myocardial ischaemia was decreased by the same amount, but verapamil was significantly more effective in prolonging the exercise time. Both drugs reduced the number of episodes of ST-segment depression during 24 hours of ambulatory electrocardiographic monitoring, which was analyzed in nine patients. It is concluded that verapamil compares very favourably with propranolol in the treatment of stable angina, and is more beneficial in improving exercise capacity.

Cardiac conduction disorders in six infants with "near-miss" sudden infant deaths

Cardiac conduction disorders caused sudden serious illnesses in six infants that might have been fatal if diagnosis and treatment had been delayed. These cases provide circumstantial evidence to support a link between cardiac conduction disorders and some sudden infant deaths. A further potential long-term effect of these disorders is illustrated in one child in whom psychomotor retardation seemed to develop after an episode of cerebral hypoxia that was probably by an arrhythmia associated with the Wolff-Parkinson-White syndrome. Cardiac conduction disorders may be detected by routine neonatal ECG screening, and it may therefore be appropriate to start prophylactic antiarrhythmic treatment in certain children before clinical signs develop.