Poisson random measure noise-induced coherence in epidemiological priors informed deep neural networks to identify the intensity of virus dynamics

Abstract

Differential equations-based epidemiological compartmental systems and deep neural networks-based artificial intelligence can effectively analyze and combat monkeypox (MPV) transmission with Poisson random measure noise into a stochastic SEIQR (susceptible, exposed, infected, quarantined, recovered) model human population and SEI (susceptible, exposed, infected) for rodent population. Compartmental models have estimates of parameter complications, whereas machine learning algorithms struggle to understand MPV's progression and lack elucidation. This research introduces Levenberg Marquardt backpropagation neural networks (LMBNNS) in training, a new approach that combines compartmental frameworks with artificial neural networks (ANNs) to explain the complex mechanisms of MPV. Meanwhile, a model description proves the existence and uniqueness of a global positive solution. A threshold parameter is determined and employed to identify the factors that lead to infection in the general public. Furthermore, other criteria are developed to eliminate the infection within the entire population. The MPV is eliminated if [Formula: see text], but continues if [Formula: see text]. The study depends on two functional scenarios to quantitatively clarify the theoretical results. An adapted dataset is generated employing the Adam algorithm to minimize the mean square error (MSE) by setting its data effectiveness to 81% for training, 9% for testing, and 10% for validation. The solver's accuracy is validated by minimal absolute error and complementing responses to every hypothetical situation. In order to verify the adaptation's reliability and precision, productivity is measured using the error histogram, changeover state, and prediction for addressing the MPV model. Visual representations are used to illustrate the investigation and compare results. Utilizing this hybrid approach, we want to increase our comprehension of disease propagation, strengthen forecasting competencies, and influence more efficient public health actions. The combination of stochastic processes and machine learning approaches creates a powerful tool for capturing the inherent uncertainties in infectious disease dynamics, as well as a more accurate framework for real-time epidemic prediction and prevention.

Keywords: Epidemiological modeling; Monkeypox virus; Neural network; Poisson random measure noise; State-space models.

Fig. 1

(a) Geographical distribution of confirmed and suspected monkeypox cases during the outbreak (Diagram generated with Datawrapper) (see) (b) The cumulative number of identified cases (by validation period) following the initial instance occurrence within the 2023 epidemic, as well as the entire amount of nations registering verified cases.

Fig. 2

Schematic flow of MPV model (1).

Fig. 3

(a) Parameter prediction: The black dots depicts the WHO prevalence rate, whereas the red curve represents the fitted curves for Portugal from 17 May 2022 and 10 January 2023. (b) As of January 10, 2023, there were cumulative and weekly occurrences of MPV, as well as infectious in Portugal. The bars show the distribution of MPV positive data by collecting date (week) and are color-coded based on virus accessibility. The line that is dashed indicates the overall amount of cases.

Fig. 4

Numerical simulations are conducted for three different case classifications matching the framework (4). These categories include the following: (1) deterministic case; (2) Gaussian white noise; (3) Poisson random measure noise.

Fig. 5

Numerical simulations are conducted for three different case classifications matching the framework (3). These categories include the following: (1) deterministic case; (2) Gaussian white noise; (3) Poisson random measure noise.

Fig. 6

Numerical simulations are conducted for three different case classifications matching the framework (3). These categories include the following: (1) deterministic case; (2) Gaussian white noise; (3) Poisson random measure noise; for = 0.5; = 0.9; = 0.9.

Fig. 7

Numerical simulations are conducted for three different case classifications matching the framework (3). These categories include the following: (1) deterministic case; (2) Gaussian white noise; (3) Poisson random measure noise; for = 0.3; = 0.45; = 0.70.

Fig. 8

(a) Layer-based structure for MPV model (3) and (b) represents the network-based structure of the MPV model (3).

Fig. 9

Graphical depiction for Case I for MSE, STs, results and EHs performances for MPV model (3).

Fig. 10

Regression analysis of Case I for MPV model (3).

Fig. 11

Graphical depiction for Case II for MSE, STs, results and EHs performances for MPV model (3).

Fig. 12

Regression analysis of Case II for MPV model (3).

Fig. 13

Graphical depiction for Case III for MSE, STs, results and EHs performances for MPV model (3).

Fig. 14

Regression analysis of Case III for MPV model (3).

Fig. 15

AE performance of the MPV model (3).

Fig. 16

Comparison of the effectiveness of the classical MPV model (3).