Vaccination strategies to lessen the impact of the spread of a disease are fundamental to public health authorities and policy makers. The socio-economic benefit of full return to normalcy is the core of such strategies. In this paper, a COVID-19 vaccination model with efficacy rate is developed and analyzed. The epidemiological parameters of the model are learned via a feed-forward neural network. A hybrid approach that combines residual neural network with variants of recurrent neural network is implemented and analyzed for reliable and accurate prediction of daily cases. The error metrics and a k-fold cross validation with random splitting reveal that a particular type of hybrid approach called residual neural network with gated recurrent unit is the best hybrid neural network architecture. The data-driven simulations confirm the fact that the vaccination rate with higher efficacy lowers the infectiousness and basic reproduction number. As a study case, COVID-19 data for the state of Tennessee in USA is used.
<abstract><p>Stochastic modeling predicts various outcomes from stochasticity in the data, parameters and dynamical system. Stochastic models are deemed more appropriate than deterministic models accounting in terms of essential and practical information about a system. The objective of the current investigation is to address the issue above through the development of a novel deep neural network referred to as a stochastic epidemiology-informed neural network. This network learns knowledge about the parameters and dynamics of a stochastic epidemic vaccine model. Our analysis centers on examining the nonlinear incidence rate of the model from the perspective of the combined effects of vaccination and stochasticity. Based on empirical evidence, stochastic models offer a more comprehensive understanding than deterministic models, mainly when we use error metrics. The findings of our study indicate that a decrease in randomness and an increase in vaccination rates are associated with a better prediction of nonlinear incidence rates. Adopting a nonlinear incidence rate enables a more comprehensive representation of the complexities of transmitting diseases. The computational analysis of the proposed method, focusing on sensitivity analysis and overfitting analysis, shows that the proposed method is efficient. Our research aims to guide policymakers on the effects of stochasticity in epidemic models, thereby aiding the development of effective vaccination and mitigation policies. Several case studies have been conducted on nonlinear incidence rates using data from Tennessee, USA.</p></abstract>
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