Modeling and Forecasting Monkeypox Cases Using Stochastic Models

Abstract

Background: Monkeypox virus is gaining attention due to its severity and spread amongpeople. This study sheds light on the modeling and forecasting of new monkeypox cases. Knowledgeabout the future situation of the virus using a more accurate time series and stochastic models isrequired for future actions and plans to cope with the challenge. Methods: We conduct a side-by-sidecomparison of the machine learning approach with the traditional time series model. The multilayerperceptron model (MLP), a machine learning technique, and the Box–Jenkins methodology, alsoknown as the ARIMA model, are used for classical modeling. Both methods are applied to theMonkeypox cumulative data set and compared using different model selection criteria such as rootmean square error, mean square error, mean absolute error, and mean absolute percentage error.Results: With a root mean square error of 150.78, the monkeypox series follows the ARIMA (7,1,7)model among the other potential models. Comparatively, we use the multilayer perceptron (MLP)model, which employs the sigmoid activation function and has a different number of hidden neuronsin a single hidden layer. The root mean square error of the MLP model, which uses a single input andten hidden neurons, is 54.40, significantly lower than that of the ARIMA model. The actual confirmedcases versus estimated or fitted plots also demonstrate that the multilayer perceptron model has abetter fit for the monkeypox data than the ARIMA model. Conclusions and Recommendation: Whenit comes to predicting monkeypox, the machine learning method outperforms the traditional timeseries. A better match can be achieved in future studies by applying the extreme learning machinemodel (ELM), support vector machine (SVM), and some other methods with various activationfunctions. It is thus concluded that the selected data provide a real picture of the virus. If thesituations remain the same, governments and other stockholders should ensure the follow-up ofStandard Operating Procedures (SOPs) among the masses, as the trends will continue rising in theupcoming 10 days. However, governments should take some serious interventions to cope withthe virus. Limitation: In the ARIMA models selected for forecasting, we did not incorporate theeffect of covariates such as the effect of net migration of monkeypox virus patients, governmentinterventions, etc.

Retrospective evaluation of short-term forecast performance of ensemble sub-epidemic frameworks and other time-series models: The 2022-2023 mpox outbreak across multiple geographical scales, July 14th, 2022, through February 26th, 2023

“…The auto regressive integrate moving average (ARIMA) model is a tool for understanding and predicting future values in a time series. It is commonly employed in forecasting financial [54][55][56] and weather [57][58][59] trends, and have become a standard benchmark in disease forecasting [17,31,[33][34][35][36][37]60,61]. ARIMA models consist of three parts: the auto-regression (AR) part involving regressing on the most recent values of the series, the moving average (MA) of error terms occurring contemporaneously and at previous times, and the integration (I) or differencing to account for the overall trend in the data and to make the time series stable.…”

“…We selected the ARIMA model as baseline, as it has been frequently evaluated against other forecasting methodologies in the context of mpox [31,[33][34][35][36][37]. Therefore, its inclusion in skill score calculations provides a more in-depth quantitative evaluation of the forecasting abilities of the n-sub-epidemic and spatial-wave frameworks against a well-vetted methodology.…”

“…Several methodologies have been employed to forecast the case trajectory of the 2022-2023 mpox epidemic in various geographical regions, including, but not limited to, models focused on human judgment [29], deep learning, and artificial intelligence models (AI) [30][31][32], machine learning models [30][31][32][33][34][35], statistical models such as auto-regressive integrated moving average (ARIMA) models [31,[33][34][35][36][37], compartmental models [38], and semi-mechanistic sub-epidemic models [16]. Performance metrics employed have mainly included variations of mean absolute error (MAE) [16,30,31,[33][34][35]37], mean squared error (MSE) [16,[30][31][32][33][34][35][36][37], and mean absolute percentage error (MAPE) [16,31,[33][34][35], with only two studies also including probabilistic measures of performance such as the weighted interval score (WIS) [16,39]. Of the studies included here, four focused on the ascending phase of the epidemic (January 2022-Mid August 2022) [29,…”

“…Performance metrics employed have mainly included variations of mean absolute error (MAE) [16,30,31,[33][34][35]37], mean squared error (MSE) [16,[30][31][32][33][34][35][36][37], and mean absolute percentage error (MAPE) [16,31,[33][34][35], with only two studies also including probabilistic measures of performance such as the weighted interval score (WIS) [16,39]. Of the studies included here, four focused on the ascending phase of the epidemic (January 2022-Mid August 2022) [29,33,34,36], four evaluated forecasts of the ascending and peak of the epidemic (February 2022-September 2022) [30][31][32]39], and four focused on the ascending, peak and decline phases of the epidemic (January 2022-Present) [16,35,37,38].…”

Voluntary vaccination may not stop monkeypox outbreak: A game-theoretic model

“…A model incorporating sexual behavior dynamics and stratifying the population into high-and low-risk groups was developed in [26]. Stochastic models and individual based simulations for the current outbreak are also being developed [27][28][29][30].…”