Monkeypox is a zoonotic infection caused by a virus that belongs to the family of Orthopoxvirus. Since the first human reported case of Monkeypox in the Democratic Republic of Congo in 1970, sporadic human cases have been identified both inside and outside of Africa [1]. On May 7, 2022, Monkeypox was detected in a traveller returning to the United Kingdom from Nigeria, with the rate of reported cases then increasing until mid-July before declining (Fig. 1a) [2].
Monkeypox virus is an infectious pathogen which can be transmitted through close physical contact and fomites. In the current worldwide outbreak, cases are predominantly amongst gay and bisexual men who have sex with men (GBMSM) with clusters of cases linked with venues where individuals were exposed to the virus through close, often sexual, contact [3]. Pre-symptomatic transmission has been found to be a significant component of this outbreak, with approximately 53% of transmission prior to symptom onset [4]. Initial symptoms can be influenza-like with reported incubation periods of 3–20 days [5] and mean incubation period of 7–9 days [5–6]. This is followed by smallpox-like rashes, which sequentially progress to macules, papules and vesicles before crusting over after 2–4 weeks [7].
The UK Health Security Agency (UKHSA) has been monitoring and responding to the Monkeypox outbreak [8]. As part of the response, our group tracked the epidemic potential and gave informed advice to aid public health policy. Amongst reported cases, a large proportion (40–80%; Fig. 1a) described developing a combination of symptoms up to a month prior to presenting to healthcare providers [8]. As the awareness of the disease increases, due to public health information or other interventions, the delays in presenting to healthcare providers may decrease. If the reporting delays decrease rapidly, it will lead to a surge in reported cases due to the concertina-effect of people at different stages of disease presenting to healthcare providers at the same time.
Estimating R(T) With Dynamic Reporting Delays
To quantify the changes in reporting delays and their effect on estimating the epidemic growth rate r(t), we developed a Bayesian model incorporating both a dynamic growth rate and dynamic delays ([9], see Supplementary Materials). We define the reporting delay as the time between the onset of symptoms and the case being reported to the UKHSA, which has been determined for a fraction of cases by follow up questionnaires. In the model, both the growth rate of symptomatic cases and the parameters of the reporting delay distributions follow Gaussian processes which allow time variations in parameter estimates. Gaussian processes were used because of their flexibility to model time varying processes and provide confidence intervals even when the underlying mechanisms for time variation are unknown. The posterior distribution of all parameters were sampled using the MCMC sampling software Stan in the R package rstan [10]. This allowed for the model to be simultaneously fit to both the daily reported cases and the line-list of cases for which the onset of symptoms was known, thus providing an estimate of r(t) corrected for changes in the reporting delays. We estimated the delay in reporting cases in the UK dropped from about 21.9 days (CrI 16.7–30.8 days) for people who developed symptoms in early May 2022, to around 9.6 days (CrI 8.6–10.8 days) for people who developed symptoms in early June and 7.8 days (CrI 7.0-8.9 days) for people who developed symptoms in August 2022 (Fig. 1b,d). There was a rapid drop in the delays throughout May 2022 when there were significant efforts to increase the public awareness of Monkeypox in the UK. The model estimates that the epidemic growth rate r(t) had a doubling time of 10.3 days (CrI 6.6–23.9 days) in early May 2022. The growth rate decreased gradually turning negative in early July (Fig. 1c and Fig. 2a, blue curve). Note that a positive growth rate r(t) corresponds to an effective reproduction number R(t) greater than 1, and a negative r(t) corresponds to R(t) less than 1. Since r(t) is the growth rate of new symptomatic cases, it will lag the growth rate of new infections by the incubation period (7–9 days [5, 6]), and the new infections would have started to decline in late June 2022. Our results are in line with an estimate of r(t)
To demonstrate the importance of accounting for dynamic delays when estimating r(t), we re-estimated r(t) using a static delay distribution (as of May 7th) with a median delay of 15 days (Fig. 2a; green curve). The resultant estimate of r(t) had a quicker doubling time of 6 days (vs 10 days) in early May 2022 compared to the estimate with dynamic delays. This was followed by a more rapid decline in r(t) throughout May 2022, leading to a slowing of the doubling time to 22 days (vs 14 days) at the end of May compared to the estimate with dynamic delays. This is likely due to the concertina-effect of more people presenting to healthcare providers in late May even if they had first developed symptoms much earlier. Further evidence of this mechanism and the ability for our model to correct for it was provided by simulation studies, which demonstrated the same elevated r(t) followed by a rapid drop when static delays were used in the re-estimation of r(t) (Figures S1, S2 and Supplementary Material).
We investigated the stability of our estimates of r(t) as new data became available by re-estimating r(t) using censored data (Fig. 2b and S2b). Estimates of r(t) were consistent at times at least 10 days prior to each censor date, however, flattened in the 10 days immediately prior to the censor date. This is because newly symptomatic cases in the final 10 days are unlikely to have reported their symptoms by the censor date, therefore the estimate of r(t) here will be dominated by its prior (i.e. Gaussian process without drift). Flattening of estimates of r(t) is in most cases the most desirable property of a statistical estimator when interpreting right censored data, corresponding to the null assumption of projecting the impact of no change in policy or dynamics to the current time.