Mathematical modeling of mpox: A scoping review

Exploring the dynamics of monkeypox transmission with data-driven methods and a deterministic model

Introduction

Mpox (formerly monkeypox) is an infectious disease that spreads mostly through direct contact with infected animals or people's blood, bodily fluids, or cutaneous or mucosal lesions. In light of the global outbreak that occurred in 2022-2023, in this paper, we analyzed global Mpox univariate time series data and provided a comprehensive analysis of disease outbreaks across the world, including the USA with Brazil and three continents: North America, South America, and Europe. The novelty of this study is that it delved into the Mpox time series data by implementing the data-driven methods and a mathematical model concurrently-an aspect not typically addressed in the existing literature. The study is also important because implementing these models concurrently improved our predictions' reliability for infectious diseases.

Methods

We proposed a traditional compartmental model and also implemented deep learning models (1D- convolutional neural network (CNN), long-short term memory (LSTM), bidirectional LSTM (BiLSTM), hybrid CNN-LSTM, and CNN-BiLSTM) as well as statistical time series models: autoregressive integrated moving average (ARIMA) and exponential smoothing on the Mpox data. We also employed the least squares method fitting to estimate the essential epidemiological parameters in the proposed deterministic model.

Results

The primary finding of the deterministic model is that vaccination rates can flatten the curve of infected dynamics and influence the basic reproduction number. Through the numerical simulations, we determined that increased vaccination among the susceptible human population is crucial to control disease transmission. Moreover, in case of an outbreak, our model showed the potential for epidemic control by adjusting the key epidemiological parameters, namely the baseline contact rate and the proportion of contacts within the human population. Next, we analyzed data-driven models that contribute to a comprehensive understanding of disease dynamics in different locations. Additionally, we trained models to provide short-term (eight-week) predictions across various geographical locations, and all eight models produced reliable results.

Conclusion

This study utilized a comprehensive framework to investigate univariate time series data to understand the dynamics of Mpox transmission. The prediction showed that Mpox is in its die-out situation as of July 29, 2023. Moreover, the deterministic model showed the importance of the Mpox vaccination in mitigating the Mpox transmission and highlighted the significance of effectively adjusting key epidemiological parameters during outbreaks, particularly the contact rate in high-risk groups.

"Mpox in MSM: Tackling Stigma, Minimizing Risk Factors, Exploring Pathogenesis, and Treatment Approaches"

Mpox is a zoonotic disease caused by the monkeypox virus (MPV), primarily found in Central and West African countries. The typical presentation of the disease before the 2022 mpox outbreak includes a febrile prodrome 5-13 days post-exposure, accompanied by lymphadenopathy, malaise, headache, and muscle aches. Unexpectedly, during the 2022 outbreak, several cases of atypical presentations of the disease were reported, such as the absence of prodromal symptoms and the presence of genital skin lesions suggestive of sexual transmission. As per the World Health Organization (WHO), as of March 20, 2024, 94,707 cases of mpox were reported worldwide, resulting in 181 deaths (22 in African endemic regions and 159 in non-endemic countries). The United States Centers for Disease Control and Prevention (CDC) reports a total of 32,063 cases (33.85% of total cases globally), with 58 deaths (32.04% of global deaths) due to mpox. Person-to-person transmission of mpox can occur through respiratory droplets and sustained close contact. However, during the 2022 outbreak of mpox, a high incidence of anal and perianal lesions among MSMs indicated sexual transmission of MPV as a major route of transmission. Since MSMs are disproportionately at risk for HIV transmission, this review discusses the risk factors, transmission patterns, pathogenesis, vaccine, and treatment options for mpox among MSM and people living with HIV (PLWH). Furthermore, we provide a brief perspective on the evolution of the MPV in immunocompromised people like PLWH.

Supercritical and homogenous transmission of monkeypox in the capital of China

Starting from May 31, 2023, the local transmission of monkeypox (Mpox) in mainland China began in Beijing. Till now, the transmission characteristics have not been explored. Based on the daily Mpox incidence data in the first 3 weeks of Beijing (from May 31 to June 21, 2023), we employed the instant-individual heterogeneity transmission model to simultaneously calculate the effective reproduction number (Re ) and the degree of heterogeneity (k) of the Beijing epidemic. We additionally simulated the monthly infection size in Beijing from July to November and compared with the reported data to project subsequent transmission dynamics. We estimated Re to be 1.68 (95% highest posterior density [HPD]: 1.12-2.41), and k to be 2.57 [95% HPD: 0.54-83.88], suggesting the transmission of Mpox in Beijing was supercritical and didn't have considerable transmission heterogeneity. We projected that Re fell in the range of 0.95-1.0 from July to November, highlighting more efforts needed to further reduce the Mpox transmissibility. Our findings revealed supercritical and homogeneous transmission of the Mpox epidemic in Beijing. Our results could serve as a reference for understanding and predicting the ongoing Mpox transmission in other regions of China and evaluating the effect of control measures.

A hybrid forecasting technique for infection and death from the mpox virus

Objectives

The rising of new cases and death counts from the mpox virus (MPV) is alarming. In order to mitigate the impact of the MPV it is essential to have information of the virus's future position using more precise time series and stochastic models. In this present study, a hybrid forecasting system has been developed for new cases and death counts for MPV infection using the world daily cumulative confirmed and death series.

Methods

The original cumulative series was decomposed into new two subseries, such as a trend component and a stochastic series using the Hodrick-Prescott filter. To assess the efficacy of the proposed models, a comparative analysis with several widely recognized benchmark models, including auto-regressive (AR) model, auto-regressive moving average (ARMA) model, non-parametric auto-regressive (NPAR) model and artificial neural network (ANN), was performed.

Results

The introduction of two novel hybrid models, HPF 1 1 and HPF 3 4 , which demonstrated superior performance compared to all other models, as evidenced by their remarkable results in key performance indicators such as root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE), is a significant advancement in disease prediction.

Conclusion

The new models developed can be implemented in forecasting other diseases in the future. To address the current situation effectively, governments and stakeholders must implement significant changes to ensure strict adherence to standard operating procedures (SOPs) by the public. Given the anticipated continuation of increasing trends in the coming days, these measures are essential for mitigating the impact of the outbreak.