Monkeypox: a model-free analysis

Abstract

Monkeypox is a zoonotic disease caused by a virus that is a member of the orthopox genus, which has been causing an outbreak since May 2022 around the globe outside of its country of origin Democratic Republic of the Congo, Africa. Here we systematically analyze the data of cumulative infection per day adapting model-free analysis, in particular, statistically using the power law distribution, and then separately we use reservoir computing-based Echo state network (ESN) to predict and forecast the disease spread. We also use the power law to characterize the country-specific infection rate which will characterize the growth pattern of the disease spread such as whether the disease spread reached a saturation state or not. The results obtained from power law method were then compared with the outbreak of the smallpox virus in 1907 in Tokyo, Japan. The results from the machine learning-based method are also validated by the power law scaling exponent, and the correlation has been reported.

Fig. 1

a Total number of monkeypox infections in the USA was plotted as a function of time from 3rd June, 2022 to 27th September 2022. b Log–Log plot of number of infections of the USA as a function of time, the two vertical lines indicate the spectrum of scale-free behavior. The data points are overlaid with a linear regression’s best fit

Fig. 2

a Total number of infections for the smallpox outbreak of Tokyo, Japan, in 1907 was plotted as a function of time from 18th December 1907 to 25th July 1908. b Log–Log plot of number of infections as a function of time, the two vertical lines indicate the spectrum of scale-free behavior. The data points are overlaid with a linear regression best fit

Fig. 3

Schematic depiction of architecture of Echo state model

Fig. 4

Prediction of monkeypox cumulative infection per day for nine most infected countries listed in the Table 1. Red solid line indicates the realtime cumulative infection data, and open blue circles represent the prediction of the test set by the ESN model and forecasting done by the ESN model is represented by green triangles extended from the predicted set

Fig. 5

Total number of monkeypox infections in all the countries that were taken for analysis is plotted as a function of time from initial infection to 4th November 2022