The number of secondary cases, i.e. the number of new infections generated by an infectious individual, is an important parameter for the control of infectious diseases. When individual variation in disease transmission is present, like for COVID-19, the distribution of the number of secondary cases is skewed and often modeled using a negative binomial distribution. However, this may not always be the best distribution to describe the underlying transmission process. We propose the use of three other offspring distributions to quantify heterogeneity in transmission, and we assess the possible bias in estimates of the mean and variance of this distribution when the data generating distribution is different from the one used for inference. We also analyze COVID-19 data from Hong Kong, India, and Rwanda, and quantify the proportion of cases responsible for 80% of transmission, $$p_{80\%}$$ p 80 % , while acknowledging the variation arising from the assumed offspring distribution. In a simulation study, we find that variance estimates may be biased when there is a substantial amount of heterogeneity, and that selection of the most accurate distribution from a set of distributions is important. In addition we find that the number of secondary cases for two of the three COVID-19 datasets is better described by a Poisson-lognormal distribution.

The number of secondary cases is an important parameter for the control of infectious diseases. When individual variation in disease transmission is present, like for COVID-19, the number of secondary cases is often modelled using a negative binomial distribution. However, this may not be the best distribution to describe the underlying transmission process. We propose the use of three other offspring distributions to quantify heterogeneity in transmission, and we assess the possible bias in estimates of the offspring mean and its overdispersion when the data generating distribution is different from the one used for inference. We find that overdispersion estimates may be biased when there is a substantial amount of heterogeneity, and that the use of other distributions besides the negative binomial should be considered. We revisit three previously analysed COVID-19 datasets and quantify the proportion of cases responsible for 80% of transmission, p80%, while acknowledging the variation arising from the assumed offspring distribution. We find that the number of secondary cases for these datasets is better described by a Poisson-lognormal distribution.

Funding Acknowledgements Type of funding sources: None. Background Telemonitoring is an intervention that has shown to improve care of heart failure (HF) patients and thus plays a major role in preventing frequent hospital visits. Purpose This study examined the impact of HF telemonitoring on unplanned hospitalization. Methods Patients admitted to the hospital for HF and who agreed to use the non-invasive telemonitoring system were candidates in the study. It measured body weight, blood pressure and heart rate each day, and an alert was made if they exceeded a certain limit. The study contained data from 97 patients. The primary endpoint was a composite of unplanned cardiovascular hospitalization and all-cause mortality. Patients were classified into three groups: hospitalized (for any of the endpoints) during the telemonitoring period (Group 1 ["monitoring failure"]), hospitalized after the telemonitoring period (Group 2), and not hospitalized (Group 3). Results Median telemonitoring period was 222 [141, 518] days. The number of patients in each group was 18, 18, and 61. Patients in Group 1 were older (75 vs. 63 years, p < 0.001) and had poorer estimated glomerular filtration rate (31 vs. 62 mL/min/1.73m2, p < 0.001) than those in Group 3. Length of hospitalization periods at the endpoint tended to be longer in Group 1 than Group 2 (8.5 [6, 14] vs. 5 [4, 10] days, p = 0.084). Conclusion If heart failure telemonitoring fails to prevent unplanned hospitalization, the length of that hospitalization period may be longer than if the unplanned hospitalization could have been prevented.