key: cord-1055144-e9rnsnw7
authors: Gautam Jamdade, Parikshit; Gautamrao Jamdade, Shrinivas
title: Modeling and Prediction of COVID-19 Spread in the Philippines by October 13, 2020, by using the VARMAX Time Series Method with Preventive Measures
date: 2020-12-11
journal: Results Phys
DOI: 10.1016/j.rinp.2020.103694
sha: 0e8bcc0746f94b00215d1f28429cc5ba9afbbfb3
doc_id: 1055144
cord_uid: e9rnsnw7

COVID-19 outbreak is the serious public health challenge the world is facing in recent days as there is no effective vaccine and treatment for this virus. It causes 257863 confirmed cases as of September 13, 2020, with 4292 deaths in the Philippines up till now. Understanding the transmission dynamics of the infection is a crucial step for evaluating the effectiveness of control measures. Owing to this, forecasts of COVID-19 cases, deaths, cases per million, and deaths per million are necessary for the Philippines. We examine the characteristics of COVID-19 affected populations based on the data provided by WHO from December 31, 2019, to September 13, 2020. In this paper, forecasts, and analysis of the COVID-19 cases, deaths, cases per million, and deaths per million were presented for 30 days ahead. The projection results are compared with the actual data values and simulated results from the VARMAX time series method. Societal growth is assessed by the median growth rate (MGR). President Rodrigo R Duterte of the Philippines has taken good steps but much more needs to be done. We suggest Philippines governments must rapidly mobilize and make good policy decisions to mitigate the COVID-19 spread. This paper mentions major contributions, current concerns, and challenges during and post COVID-19 epidemic in the Philippines with few non-considered measures to reduce the spread of the COVID-19.

The epidemic of the COVID-19 is increasing day by day severely affecting a large population in the world [1] . Densely populated areas of countries and highly mobile populations are affected mostly showing larger transmission growth [2] . COVID-19 pandemic has damaged human lives and health. It exposes the weak health infrastructure of the countries of the world affecting the world economy.

Millions of people have lost their jobs in the past few months. The lower down transmission rate is the most difficult job in the COVID-19 epidemic [3] . WHO declared the spread of COVID-19 as a public health emergency, and the confirmed cases continued to rise globally [4] . Forecasting and analysis of COVID-19 spread is the biggest challenge for forecasters and modelers, as limited data is available to characterize early growth trajectory and its analysis, which enables the countries to respond to the outbreak. There are various statistical models used to forecast the data used for different applications [5] [6] [7] . The transmission model is formulated for forecast and analysis of COVID-19 must rely on the total number of infected, total deaths, and prediction of these. This information can be useful to health agencies to make decisions to lower down the spread [8] . Various researchers used numerous models for predictions of the COVID-19 epidemics having large variations in results [9] [10] [11] [12] . The impact of immigrants on the dynamics and control of HBV infection is studied by using optimal control theory which provides the best strategies to lower down infectious diseases in the population at the minimal possible cost. Several effective optimal control models for infectious diseases have been developed [16] [17] [18] . The FO derivative application is used in the modeling of electrical systems. The dynamics of hepatitis B and E has been modeled using different FO operators with the effect of hospitalizations in [19, 20] .

The Philippine Department of Health (DOH) confirmed its first case of COVID-19 on January 20, 2020. The Philippines was already declared the Enhanced Community Quarantine (ECQ) in NCR, Region 3 (excluding Aurora), Region 4-A, and the provinces like Pangasinan, Benguet, the Island of Mindoro, Albay, Catanduanes, Antique, Iloilo, Cebu, and Davao del Norte. The enhanced community quarantine (ECQ) involves a temporary suspension of classes, work-from-home, and skeletal or limited workers, and restriction of the population to their homes. It allows only essential services like health care, food supply, medicines, and banking during the ECQ. The doctor-to-patient ratio is poor in the Philippines, having one doctor per 33,000 patients, and one hospital bed is available to every 1,121 patients.

Cumulative confirmed case data for the COVID-19 was taken from the WHO site from December 31, 2019, to September 13, 2020. In this study, total COVID-19 cases, total COVID-19 cases per million, total COVID-19 deaths, and total COVID-19 deaths per million are forecasted for 30 days ahead from September 13, 2020, for taking decisions and doing preparation for COVID-19 epidemics.

To understand the COVID-19 epidemic, we need accurate data of confirmed cases of the infected people. But some infected people may not have symptoms, as well as people who do not carry laboratory tests and those who are misdiagnosed. In such scenarios, confirmed COVID-19 cases are only a fraction of the total infected peoples. So, model parameters cannot be accurately calculated from the COVID-19 data resulting in non-accurate predictions. Due to this normal distribution model is used. The mean, standard deviation, skewness, and kurtosis of COVID-19 data are calculated and analyzed.

The Normal distribution CDF (Cumulative Density Function) is .

(1)

The Normal distribution PDF (Probability Density Function) is

Where μ is the sample mean and σ is the standard deviation of COVID-19 data.

The CDF of the COVID-19 data provides information about the fraction of time or probability that the COVID-19 data has a particular value or lower than a particular value which is useful for determining the COVID-19 data parameters and their variations. Figure 1 shows the PDF and CDF plots for total COVID-19 cases with upper and lower bounds (95% CI) while figure 2 shows the PDF and CDF plots for total COVID-19 deaths with the upper and lower bounds. Also figure 3 shows the PDF and CDF plots for total COVID-19 cases per million with upper and lower bounds with figure 4 showing the PDF and CDF plots for total COVID-19 deaths per million with upper and lower bounds.

The PDF observed from Fig. 1a 

The VARMAX time series method stands for Vector Autoregressive Moving Average with an exogenous time series method. It is used as an epidemic model for the evaluation of infectious disease spread and used for forecasting.

A simple algorithm for determining the VARMAX model is given below. Let consider a k-variate time-series Y t induced by linearly mixed stochastic and controlled inputs:

We assume that the model is stationary and invertible. 

We now separate the current and past elements of y, and a t in equation 3:

,

Using the above definitions we may reformulate equation 5 as follows:

The model orders are estimated by the algorithm consisting of two major stages. In stage 1, the optimal lag orders for yt, xt, and at are calculated. In stage 2 the optimal lag orders are used as fixed values in an iterative calculation of the system matrices Ø i , θ j , and β k .

Stage 1. Estimating p, q, and r.

Stage 1, consists of two steps. In Step 1, we calculate optimal lag orders for the endogeneous and exogenous vectors, i.e. the parameters s and r. In Step 2, we decompose s into the lag order p for the endogeneous vector and the lag order q for the residual process.

Step 1. Determining the (s, r) order.

For each combination of s = 0, 1, ... and r = 1, 2 , . . . , we:

(i) Build the matrices, Y s , X r and , rm)

Here we select the combination (s, r) which minimizes AIC. This gives an estimate of the true order r of the X matrix. In calculating the OLS estimates γ we can use a method of adding/deleting variables.

Let the matrix of residuals e, obtained for the chosen (s, r) order, a(0). These residuals are then used to estimate the orders p and q and a new parameter vector δ as following way:

Step 2. Determining the (p, q) order.

We note that the residuals a(0) of Step 1 remain unchanged in all regressions of Step 2. For each combination of p = 0, 1,… and q = 0, 1,...around the reference point s = p + q, we:

(i) Build the matrices Y p as above,

) ( cov t e e   (iii) Estimate the Schwartz-Rissanen (SR) criterion

We then choose that combination (p*, q*) which minimizes SR and set

Next, let j = 1 and proceed to Step 2 of stage 2.

When j = 1 the parameter values are inherited from stage 1.

Stage 2. Iterative estimation of model parameter values, given the optimal lag orders p, q, and r.

Step 1. Calculating the iteration .

(10)

Step 2. Calculating new parameter estimates.

Let and )) ( ),...., Many researchers with the help of doubling rate as a tool try to access the measures of COVID-19 spread in terms of the time period (days). But doubling the rate becomes ineffective for countries having a large population as the infected population becomes large like the USA, India, Russia, and Brazil, etc. To access societal growth, we are using a median growth rate (MGR) where growth is expressed in terms of the time period which was determined by time (days) taken to have value 1.5 times that of the previous number of COVID-19 cases. In the case of the Philippines currently, MGR is 17 days.

Here discussion was presented based on the results involving the impact of control measures taken by the Philippine, major contribution, current concerns, and challenges of the COVID-19 epidemic with control measures.

In the world, various countries are taking steps and measures to counter the COVID-19 epidemic (B. 

Major contributions during the COVID-19 epidemic done by the Philippines are  President Rodrigo R Duterte's leadership take a good decision for curbing the spread 

Mathematical modeling is a tool for analyzing, assessing, and predicting the scale and time course of COVID-19 epidemics, and evaluating the effectiveness of public health measures and policies. In the present work, we use a VARMAX time series method to analyze the dynamics of COVID-19. The model is further used to estimate the parameters of COVID-19 like net the total COVID-19 cases, net total COVID-19 deaths, net total COVID-19 cases per million, and net total COVID-19 deaths per million using the reported infected cases documented in the Philippines from December 31, 2019, to September 13, 2020. The ordinary least squares algorithm is used for parameter estimation. The findings show that the model simulated infected values are in good agreement with the reported COVID-19 infected cases. As per the VARMAX time series method, on October 13, 2020, net the total COVID-19 cases, net total COVID-19 deaths, net total COVID-19 cases per million, and net total COVID-19 deaths per million after 30 days will be 632863, 6632, 5853, and 60 respectively in the Philippines. In the case of the Philippines, the median growth rate of COVID-19 spread is 17 days.

These forecasts are beneficial for real-time preparation for anticipating the required number of hospital beds and other medical resources needed to prepare in the coming days. This paper mentions major contributions, current concerns, and challenges during and post COVID-19 epidemic in the Philippines. Few non-considered measures, if implemented in the Philippines, will reduce the spread of the COVID-19.

Authors claim no conflict of interests.

None. This research received no specific grant from any funding. 

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