The type III functional response has historically been associated with switching predators; when there is a choice of prey the predator favors the more abundant prey type. Although this functional response has been found in experiments where both prey densities are manipulated, in real world studies the type II functional response is more commonly found. In modeling, the type III functional response is often used in systems where the second prey type is, implicitly, assumed to be constant. Here we define a functional response that takes into account both prey densities. This causes the functional response to show both type II and type III behavior, dependent on the interaction between the two prey densities. If we take into account population dynamics, we find a type II functional response in most cases, because predation regulates the relative prey densities. This explains why type III functional responses are found in experiments where both prey densities are manipulated, but type II functional responses occur when the feedback of population dynamics on the functional response is important. Furthermore, the results show that switching can have a stabilizing or destabilizing effect and can even lead to predator extinction.

England has been heavily affected by the SARS-CoV-2 pandemic, with severe ‘lockdown’ mitigation measures now gradually being lifted. The real-time pandemic monitoring presented here has contributed to the evidence informing this pandemic management throughout the first wave. Estimates on the 10 May showed lockdown had reduced transmission by 75%, the reproduction number falling from 2.6 to 0.61. This regionally varying impact was largest in London with a reduction of 81% (95% credible interval: 77–84%). Reproduction numbers have since then slowly increased, and on 19 June the probability of the epidemic growing was greater than 5% in two regions, South West and London. By this date, an estimated 8% of the population had been infected, with a higher proportion in London (17%). The infection-to-fatality ratio is 1.1% (0.9–1.4%) overall but 17% (14–22%) among the over-75s. This ongoing work continues to be key to quantifying any widespread resurgence, should accrued immunity and effective contact tracing be insufficient to preclude a second wave. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.

A prospective epidemiological survey on bovine respiratory syncytial virus (BRSV) infections in calves was carried out on 21 dairy farms during one BRSV epidemic season. Special attention was paid to the role of maternal antibodies. On 15 farms the spread of the virus was demonstrated during the investigation period and on eight farms this was accompanied by an outbreak of acute respiratory disease. Disease seldom occurred in calves younger than two weeks old and the most severe disease was observed in calves from one to three months old. Although maternal antibodies did not effectively prevent the disease, both the incidence and severity of disease were inversely related to the level of specific maternal antibodies. Two serodiagnostic techniques were compared. In calves older than three months from herds with disease outbreaks associated with bovine respiratory syncytial virus the diagnosis was established in 80 per cent of the animals by an increase in IgG titre against BRSV and in 77 per cent by the detection of BRSV specific IgM. In comparison, only 10 per cent of the calves younger than three months were positive by IgG serodiagnosis, and 51 per cent by IgM serodiagnosis. On farms where the spread of the virus was accompanied by an outbreak of clinical disease more calves were present, a higher proportion of the calves was younger than three months, and calves of all ages were more often housed together.

This paper is concerned with the application of recent statistical advances to inference of infectious disease dynamics. We describe the fitting of a class of epidemic models using Hamiltonian Monte Carlo and Variational Inference as implemented in the freely available Stan software. We apply the two methods to real data from outbreaks as well as routinely collected observations. Our results suggest that both inference methods are computationally feasible in this context, and show a trade-off between statistical efficiency versus computational speed. The latter appears particularly relevant for real-time applications.

ABSTRACT. We develop a theory for the food intake of a predator that can switch between multiple prey species. The theory addresses empirical observations of prey switching and is based on the behavioural assumption that a predator tends to continue feeding on prey that are similar to the prey it has consumed last, in terms of, e.g., their morphology, defences, location, habitat choice, or behaviour. From a predator's dietary history and the assumed similarity relationship among prey species, we derive a general closed-form multi-species functional response for describing predators switching between multiple prey species. Our theory includes the Holling type II functional response as a special case and makes consistent predictions when populations of equivalent prey are aggregated or split. An analysis of the derived functional response enables us to highlight the following five main findings.(1) Prey switching leads to an approximate power-law relationship between ratios of prey abundance and prey intake, consistent with experimental data. (2) In agreement with empirical observations, the theory predicts an upper limit of 2 for the exponent of such power laws. (3) Our theory predicts deviations from power-law switching at very low and very high prey-abundance ratios. (4) The theory can predict the diet composition of a predator feeding on multiple prey species from diet observations for predators feeding only on pairs of prey species. (5) Predators foraging on more prey species will show less pronounced prey switching than predators foraging on fewer prey species, thus providing a natural explanation for the known difficulties of observing prey switching in the field.