Mathematical modelling and time series clustering of Mpox outbreak: A comparative study of the top 10 affected countries and implications for future outbreak management

Abstract

The 2022 Mpox outbreak, characterized by its rapid cross-continental spread beyond traditionally endemic regions, presented a renewed threat to global health security. This study presents a comparative epidemiological analysis of the ten countries most affected by Mpox, integrating mathematical modelling with time series clustering, the first of its kind to analyze the 2022 WHO Mpox data. By applying an SIR-based model to estimate the effective transmission rate, basic reproduction number, time of first infection, and initial susceptible population, the study captures both the pace and persistence of Mpox spread, while critically assessing the effectiveness of national public health responses. Key findings reveal a paradox in North America: Canada exhibited a high transmission rate but a low reproduction number, indicating an elevated transmission potential per contact alongside limited secondary spread. This is likely due to concurrent containment measures or behavioral factors. In contrast, the United States, despite having a lower initial transmission rate, recorded a higher reproduction number. Similarly, Germany exhibited a similar risk trajectory, with elevated reproductive numbers despite robust infrastructure. The cases in the USA and Germany are likely due to systemic health and socio-political policy gaps and delayed behavior-targeted interventions, particularly in the population of men having sex with men (MSM). In Latin America, countries such as Peru and Mexico suffered disproportionately, likely due to limited access to healthcare, which compounded transmission dynamics and reproductive potential. Our study demonstrates that effective Mpox control is not solely dependent on health infrastructure, but also on behavioral targeting, equity, and adaptive health governance. This calls for cross-country and intercontinental collaborations towards combating current and future health shocks, including epidemics.

Keywords: Bootstrapping; Clustering; Dynamic Time Warping; Epidemics; Health shocks; Mpox virus.

Fig. 1

Total Cases of Mpox Outbreak Per Country ([7] data).

Fig. 2

Time Series Progression for Mpox in the top 10 countries on the same scale. Note: Fig. 2 indicates an outbreak, but similarities are hard to discern on the same scale. Initial outbreak dates and peak levels vary by country. In Fig. 3, plotting each country's data on its own scale shows defined peaks, with the outbreak lasting longer at the peak in some countries. The U.S.A. and Germany have similar peak shapes, indicating a steady rise and fall, while Brazil and the U.K. have longer-lasting peaks.

Fig. 3

Time Series Progression for Mpox in the top 10 countries on the different scales.

Fig. 4

Compartmental diagram of the SIR model.

Fig. 5

Compartmental diagram of the SEIR model.

Fig. 6

Graph of United States Mpox data with Optimal Parameters.

Fig. 7

Residual Plot of United States Mpox data with Optimal Parameters.

Fig. 8

SIR Model Fits to 2022 Mpox Data for Top 10 Countries.

Fig. 9

Comparison of Parameter Values for $\beta$ and $S_0$ .

Fig. 10

Comparison of Mpox Trends Across Countries.

Fig. 11

Dendrogram of Countries Based on Time Series Data.

Fig. 12

Clustering Results on Scaled Mpox Data.