This paper proposes a varying coefficient Susceptible-Exposed-Infected-Removed (vSEIR) model to dynamically simulate the early mpox epidemic that sparked panic in 2022, considering the time-varying infection rate and the group protected by the smallpox vaccination. We apply the recursive least squares algorithm with a forgetting factor for real-time identification of time-varying infection rates and the efficacy of non-pharmacological interventions. The sparse Hodrick-Prescott (HP) filter, tuned with leave-one-out cross-validation, captures mpox epidemic kinks via the effective reproduction number R t obtained from the discrete vSEIR model. We experiment with this approach in Brazil, Spain, UK and US, comparing COVID-19 and mpox outbreaks based on those kinks and transmission cycles, identifying that except for Spain, mpox epidemic reached its decline period earlier than COVID-19 without strong interventions. Additionally, the result regarding sensitivity analyses shows that the total number of mpox outbreak infections would have increased by 12% without smallpox vaccination and the data uncertainty can bring great variations in R t .