### Introduction

### Methods

### COVID-19 confirmed cases data

### Prediction models

### Segmented Poisson model

*t*based on a segmented Poisson model. Let

*Y*be the confirmed cases at day

_{t}*t*which is the number of days since the first case occurred. Poisson model is defined as;

*μ*is the expectation of

_{t}*Y*with segments.

_{t}*c*(

_{i}*i*=1,2,3) are breakpoints.

### NB model

*λ*is the conditional expectiation of

_{t}*Y*given

_{t}*F*

_{t-1}as the history of the joint process {

*Y*,

_{t}*λ*:

_{t}*t*∈ℕ}. Conditional mean and variance of

*Y*are defined as;

_{t}*ϕ*is the dispersion parameter. And overdispersion parameter

*σ*

^{2}is defined as

*σ*

^{2}=1/

*ϕ*. NBdistribution is defined as;

*y*=0,1,…

*n*. For estimating

*λ*,

_{t}*l*={1,7,21} were used as lagged confirmed cases and

### LLR model

*h*, which is the number of the nearest past observations to be used in the local fit. We use tricube kernel of weight W(u)=(1-|u|

^{3})

^{3}for each point. The local quadratic log-likelihood is defined as;

*l*are the log-likelihood function based on Poisson distribution assumption. The local likelihood estimate is made by maximizing over the parameter

*a*=(

*a*

_{0},

*a*

_{1},

*a*

_{2})

^{t}.

### Long short-term memory

*X*be as a set of vector consisting of

_{t}*Y*to

_{t-h}*Y*according to day

_{t-1}*t*, where

*h*is the bandwidth having values {7, 14, 21, 28, 35, 42, 49, 56}. Among these, the optimal

*h*is selected using validation set, which is last 7 days of the training period. The data is normalized using minmax normalizer to transform data to be in the range of 0 to 1.

*X*with

_{t}*C*

_{t-1}and

*h*

_{t-1}to be trained. The

*C*

_{t-1}and

*h*

_{t-1}are the state and output of the last block, respectively. We assume four blocks with 64 units, each with a 0.2 dropout layer. The optimization is held using the adam optimizer to minimize the MSE during the training process.

### SEIR model with least squares

*β*is the transmission rate,

*γ*is the recovery rate, and 1/κ is the average incubation period. The initial condition of this model

*S(0)*,

*E(0)*,

*I(0)*,

*R(0)*must satisfy the condition

*S(0)*+

*E(0)*+

*I(0)*+

*R(0)*= N, where N is the total population size. In data fitting, the unknown parameters in model were estimated by a least squares algorithm. The numerical simulation and analysis were performed in MATLAB 2020a.

### Gradient boosting machine

*F*is the updated model,

_{m}*F*

_{m-1}is previous model and

*ρ*

_{m}*h*is the newly added model.

_{m}*h*is the trained base learner which minimizes the loss function L and

_{m}*ρ*is the multiplier which is found by solving one dimensional optimization problem.

### Model assessment

*n*is the number of data points,

*y*is the observed values,

_{t}