Estimating Time-Dependent COVID-19 Parameters Using Kolmogorov-Arnold Network and Fourier Series

We introduce a novel method for estimating COVID-19 time-varying parameters.

These parameters are in the context of an SIRD compartmental differential equations.

The time-dependent parameters are the transmission rate $\beta(t)$, recovery rate $\gamma(t)$, and mortality rate $\mu(t)$.

The method harnesses the novel Kolmogorov-Arnold Network (KAN), which is a type of artificial neural network.

In KAN, we learn activation functions that are represented using Fourier series, hence the abbreviation KAN-F.

We define three KAN-F functions $\widehat{\beta}$, $\widehat{\gamma}$, $\widehat{\mu}$ that model the true parameters $\beta(t)$, $\gamma(t)$, $\mu(t)$, respectively.

The objective loss function that has to be minimized is subject to Physics-Informed Neural Network (PINN) or Epi-DNN.

We estimate the COVID-19 time-dependent parameters using COVID-19 data of three South-East Asian countries: Indonesia, Singapore, Malaysia.

The time period of choice for the data coincides with the period where SARS-CoV-2 Delta variant (B.1.617.2) was dominant.

Using Epi-DNN and KAN-F, we are able to estimate $\beta(t)$, $\gamma(t)$, and $\mu(t)$, with decent accuracy and comparative efficiency.

The total number of training epochs for Indonesia is 4316 steps, for Singapore is 8408 steps, and for Malaysia is 8000 steps.

For all countries, each of the three functions $\widehat{\beta}$, $\widehat{\gamma}$, and $\widehat{\mu}$ has the same KAN-F architecture of 2 hidden layers.

Specifically, we implement 8 input neurons, 17 neurons for the first hidden layer, 35 neurons for the second hidden layer, and 1 output neuron.

The number of Fourier terms for each activation function is $30$.