Effective Reproduction Number

Measuring and visualizing the effective reproduction number for various epidemics

When infection is spreading through a population, it is often convenient to work with the effective reproduction number R, which is defined as the actual average number of secondary cases per primary case. The value of R reflects the impact of control measures and depletion of susceptible persons during the epidemic. If R exceeds 1, the number of cases will inevitably increase over time, and a large epidemic is possible. To stop an epidemic, R needs to be persistently reduced to a level below 1 .

We can visualize the epidemic curve for in and its respective reproduction number based on as follows:

The shown epidemic curve comprises all captured cases and their effective reproduction number assigned to their given or estimated symptom onset date. The saturation curve shows the limited growth trend converging towards its saturation barrier .

It is possible to obtain likelihood-based estimates of R. The relative likelihood p_{ij} that case i has been infected by case j, given their difference in time of symptom onset t_i-t_j, can be expressed in terms of the probability distribution for the generation interval. This distribution for the generation interval is available for many infectious diseases, and we denote it by w(\tau). The relative likelihood that case i has been infected by case j is then the likelihood that case i has been infected by case j , normalized by the likelihood that case i has been infected by any other case k: \Large p_{ij}= \frac{w(t_i-t_j)}{\displaystyle\sum_{{i} \ne {k}} w(t_i-t_k)}

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