Accumulation of Immunity in Heavy-Tailed Sexual Contact Networks Shapes Mpox Outbreak Sizes

Abstract

Many countries affected by the global outbreak of mpox in 2022 have observed a decline in cases. Our mathematical model accounting for heavy-tailed sexual partnership distributions suggests that mpox epidemics can hit the infection-derived herd immunity threshold and begin to decline, with <1% of sexually active men who have sex with men infected regardless of interventions or behavioral changes. We consistently found that many countries and US states experienced an epidemic peak, with cumulative cases of around 0.1% to 0.5% among men who have sex with men. The observed decline in cases may not necessarily be attributable to interventions or behavioral changes primarily.

Keywords: depletion of susceptibles; heavy-tailed network; herd immunity; men who have sex with men; mpox.

Figure 1.

The observed and modeled number of cumulative mpox cases per MSM population. Estimated CIPP range by (A) country and (B) US state. We fitted Gompertz curves to the cumulative reported case count over time in each country and US state and estimated the cumulative number of mpox cases per MSM population size by the apparent epidemic peak, where the estimated daily epidemic growth rate is consistent with a near-zero value (ie, within ±0.01). Some countries or US states have not clearly passed the peak as of available data (last updated 15 October 2022 for countries and 15 March 2023 for US states); therefore, the upper CIPP limit is undetermined (blue bars connecting to dotted lines). Others have apparently passed the peak and have both CIPP limits (red bars). The consensus range of CIPP (values consistent with at least 50% of included countries/states) is shown with light blue shades. C, Modeled trajectory of the effective reproduction number ($R_{\mathrm{eff}}$) over the course of an epidemic. The reproduction number was computed for 3 possible values of SAR (0.1, 0.2, and 0.3, from bottom to top). D, Estimated relationship between CIPP and SAR. Thick (narrower) and thin green (wider) areas represent the global and US consensus ranges of CIPPs, respectively. CIPP, cumulative incidence proportion at a peak of an epidemic; MSM, men who have sex with men; SAR, secondary attack risk.

Figure 2.

Estimated peak and final sizes by secondary attack risk in the absence of effective interventions or behavioral changes. Cumulative numbers of cases per MSM population at the peak and end of an epidemic are shown, as estimated by our model accounting for heavy-tailed sexual partnership distribution and infection-derived immunity. For comparison, a dotted line representing double the outbreak size at the peak is also included. MSM, men who have sex with men.