Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom

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.

Comparative Epidemiological Assessment of Monkeypox Infections on a Global and Continental Scale Using Logistic and Gompertz Mathematical Models

The monkeypox virus (MPXV) has caused an unusual epidemiological scenario-an epidemic within a pandemic (COVID-19). Despite the inherent evolutionary and adaptive capacity of poxviruses, one of the potential triggers for the emergence of this epidemic was the change in the status of orthopoxvirus vaccination and eradication programs. This epidemic outbreak of HMPX spread worldwide, with a notable frequency in Europe, North America, and South America. Due to these particularities, the objective of the present study was to assess and compare cases of HMPX in these geographical regions through logistic and Gompertz mathematical modeling over one year since its inception. We estimated the highest contagion rates (people per day) of 690, 230, 278, and 206 for the world, Europe, North America, and South America, respectively, in the logistic model. The equivalent values for the Gompertz model were 696, 268, 308, and 202 for the highest contagion rates. The Kruskal-Wallis Test indicated different means among the geographical regions affected by HMPX regarding case velocity, and the Wilcoxon pairwise test indicated the absence of significant differences between the case velocity means between Europe and South America. The coefficient of determination (R2) values in the logistic model varied from 0.8720 to 0.9023, and in the Gompertz model, they ranged from 0.9881 to 0.9988, indicating a better fit to the actual data when using the Gompertz model. The estimated basic reproduction numbers (R0) were more consistent in the logistic model, varying from 1.71 to 1.94 in the graphical method and from 1.75 to 1.95 in the analytical method. The comparative assessment of these mathematical modeling approaches permitted the establishment of the Gompertz model as the better-fitting model for the data and the logistic model for the R0. However, both models successfully represented the actual HMPX case data. The present study estimated relevant epidemiological data to understand better the geographic similarities and differences in the dynamics of HMPX.

A nonlinear fractional epidemic model for the Marburg virus transmission with public health education

In this study, a deterministic model for the dynamics of Marburg virus transmission that incorporates the impact of public health education is being formulated and analyzed. The Caputo fractional-order derivative is used to extend the traditional integer model to a fractional-based model. The model's positivity and boundedness are also under investigation. We obtain the basic reproduction number [Formula: see text] and establish the conditions for the local and global asymptotic stability for the disease-free equilibrium of the model. Under the Caputo fractional-order derivative, we establish the existence-uniqueness theory using the Banach contraction mapping principle for the solution of the proposed model. We use functional techniques to demonstrate the proposed model's stability under the Ulam-Hyers condition. The numerical solutions are being determined through the Predictor-Corrector scheme. Awareness, as a form of education that lowers the risk of danger, is reducing susceptibility and the risk of infection. We employ numerical simulations to showcase the variety of realistic parameter values that support the argument that human awareness, as a form of education, considerably lowers susceptibility and the risk of infection.

Mathematical assessment of monkeypox disease with the impact of vaccination using a fractional epidemiological modeling approach

This present paper aims to examine various epidemiological aspects of the monkeypox viral infection using a fractional-order mathematical model. Initially, the model is formulated using integer-order nonlinear differential equations. The imperfect vaccination is considered for human population in the model formulation. The proposed model is then reformulated using a fractional order derivative with power law to gain a deeper understanding of disease dynamics. The values of the model parameters are determined from the cumulative reported monkeypox cases in the United States during the period from May 10th to October 10th, 2022. Besides this, some of the demographic parameters are evaluated from the population of the literature. We establish sufficient conditions to ensure the existence and uniqueness of the model's solution in the fractional case. Furthermore, the stability of the endemic equilibrium of the fractional monkeypox model is presented. The Lyapunov function approach is used to demonstrate the global stability of the model equilibria. Moreover, the fractional order model is numerically solved using an efficient numerical technique known as the fractional Adams-Bashforth-Moulton method. The numerical simulations are conducted using estimated parameters, considering various values of the fractional order of the Caputo derivative. The finding of this study reveals the impact of various model parameters and fractional order values on the dynamics and control of monkeypox.

Modelling the impact of vaccination and environmental transmission on the dynamics of monkeypox virus under Caputo operator

In this study, we examine the impact of vaccination and environmental transmission on the dynamics of the monkeypox. We formulate and analyze a mathematical model for the dynamics of monkeypox virus transmission under Caputo fractional order. We obtain the basic reproduction number, the conditions for the local and global asymptotic stability for the disease-free equilibrium of the model. Under the Caputo fractional order, existence and uniqueness solutions have been determined using fixed point theorem. Numerical trajectories are obtained. Furthermore, we explored some of the sensitive parameters impact. Based on the trajectories, we hypothesised that the memory index or fractional order could use to control the Monkeypox virus transmission dynamics. We observed that if the proper vaccination is administrated, public health education is given, and practice like personal hygiene and proper disinfection spray, the infected individuals decreases.