On parameter estimation approaches for predicting disease transmission through optimization, deep learning and statistical inference methods

Abstract

In this paper, we consider compartmental disease transmission models and discuss the importance of determining model parameters that provide an insight into disease transmission and prevalence. After a brief review and comparison of the performance of some heuristic approaches, the paper introduces three approaches including an optimization approach, a physics informed deep learning and a statistical inference method to estimate parameters and analyse disease transmission. The deep learning framework utilizes the hidden physics of infectious diseases and infer the latent quantities of interest in the model by approximating them using deep neural networks. The performance of the deep learning method is validated against representative small and big data sets corresponding to a well-known benchmark example and the results indicate that deep learning is a viable candidate to determine model parameters. The paper also presents the need for researchers to understand different types of dependencies exhibited in a typical data set and discovering the most appropriate approaches for statistical inference. Specifically, in this work we apply a time-series inferential method with a variety of statistical models. Our results indicate the efficiency and importance of statistical inference methods for researchers to understand and analyse time-series data to make confident predictions.

An SIER model to estimate optimal transmission rate and initial parameters of COVD-19 dynamic in Sri Lanka

“…(1) , (2) , (3) , (4) is solved to estimate the parameters and matching with reported COVID-19 cases in Sri Lanka in the first 80 days of its outbreak. Numerical schemes presented in [20] , [21] , [22] , [16] are coupled with Runge–Kutta method of order four to carry out the simulation of the problem in optimization. The algorithm stops once the termination condition is satisfied.…”

“…We define the following least-squares functional for the matching between simulated output from system Eqs. (1) , (2) , (3) , (4) and the reported data for the period of eighty days since the first local COVID-19 case was identified during the second week of March 2020 [16] , [17] . where for is the time series of clinically identified COVID-19 commutative cases in Sri Lanka and that should be matched with the sum of simulated results for infected and recovered for .…”

Forecasting Malaysia COVID-19 Incidence based on Movement Control Order using ARIMA and Expert Modeler

“…It is widely used not just in economic sectors but also in health. 8 A systematic review on forecasting influenza outbreak have shown some degree of accuracy despite various technique that is being used. 7 These forecasting techniques are useful for prediction of new cases to help planning in prevention and control measure.…”

“…7 There are few methods that can be used for forecasting such as compartmental model, deep learning and time series. 8 The most widely popular technique used the basic compartmental model such as SIR model which is based on susceptible, infectious and recovered classes and the functions of each of this compartment change with time. Secondly the deep learning method or neural networks which utilize the emergence of big data.…”

“…Most of current predictions focus on SIR models which is the Edre MA, Muhammad Adil ZA, Jamalludin AR Department of Community Medicine, Kulliyyah of Medicine, International Islamic University Malaysia simplest form of the compartmental models of Susceptible(S), Infected(I) and Recovered(R). 8 However, these models require a lot of assumptions and could be misleading. The more complex models of SIR in fact require more parameters and thus become less reliable in predictions.…”