A Pair Formation Model with Recovery: Application to Monkeypox

Abstract

The current global outbreaks of Monkeypox is a unique infectious disease in the way it seems to be transmitting: it has been observed to be highly concentrated in communities of men who have sex with men (MSM) through pair formation, and also provides immunity. This framework of mostly close, prolonged contact spreading a disease that admits immunity after infection is unlike similar infections which either offer little to no immunity post-infection or are lifelong infections. This creates the need for a new model framework that incorporates pair formation structure with recovery. While seemingly a straight forward model, we show how new dynamics arise from the combination of pair formation and recovery that are not present in a standard model with recovery and also not present in a pair formation model without recovery. We see that the combination of these two properties allows for waves of infection that are not seen in a standard SIR model. These dynamics suggest that outbreaks of monkeypox around the world may require special attention from public health. We also derive a reproduction number for this model and estimate the reproduction number of human monkeypox to be ≈2.3 using global and Canadian data. The expression derived for R0 can help estimate key parameters for diseases transmission and public health interventions and compare to equivalent models without pair formation.

Adaptive changes in sexual behavior in the high‐risk population in response to human monkeypox transmission in Canada can help control the outbreak: Insights from a two‐group, two‐route epidemic model

“…A number of mathematical models have been devised to shed light on the current monkeypox transmission dynamics. Betti et al 52 developed a new modeling framework that incorporates a modified standard SIR model and pair formation structure with recovery. They show that this model can outperform the standard models with recovery.…”

Monkeypox: A review of epidemiological modelling studies and how modelling has led to mechanistic insight

“…The model has been validated and applied to understand the transmission potential of mpox in unvaccinated populations [53]. Bhunu & Mushayabasa [54] presented a basic SIR compartmental model to examine the transmission dynamics of mpox between humans and non-humans, and Betti et al [55] present a SIR model with additional pair-formation dynamics to account for transmission via prolonged close contact between individuals.…”

“…Data-driven individual-level and population-level modelling studies can be used to outline the importance of public health policies and various mitigation strategies. For example, the model presented by Betti et al [55] presents a novel framework that includes pair-formation (accounting for prolonged close contact between people) to describe mpox transmission. They show their pair-formation model captures population trends in data with an estimated R 0 of 2.3, and they further predict the occurrence of future waves of infection.…”

“…For example, based on Canadian mpox trends, there are predicted to be further peaks occurring on an approximately annual basis [55]. Yuan et al consider an SEIR model whereby the population is divided into high and low risk and focus their study on mass gathering scenarios [70].…”

“…At the population level, mathematical modelling leverages population-metrics such as contact tracing data, cumulative case counts, and wastewater surveillance to predict outbreak characteristics such as recovery rates, transmission, virulence, and reproduction numbers. Although the current mpox epidemic case counts are on the decline, models are currently predicting future waves to occur on an annual scale [55]. Thus, modelling efforts can be used to allocate public health resources to curb the future spread of infection, such as when and who to target in vaccine or education campaigns.…”