﻿Trend Analysis Modelling and Prediction of Epidemic COVID-19 for US, Italy, Spain and Pakistan

The evidence of Covid19 outbreak was first received in December 2019 in China and it spread out rapidly on the map of the world. The cases of Coronavirus are increasing day by day around the world due to which mortality rate raises hastily. In the matter of days, WHO declared Covid19 as pandemic of the decade. So far, it is controlled by taking strict precautions in terms of lockdown and supervised treatments at the hospital. As its epidemic is severely breaking the scale, there is a necessity to recognize and evaluate its extension in people on each new day. We collected time series data from January 22, to April 28, 2020 which includes the number of confirmed patients (CP) and reported deaths (RD) of 186 countries all around the world. We choose to evaluate the data for US, Italy, Spain and Pakistan. We are selecting here the data up to April 28, 2020, however the data is automatically updated from Humanitarian Data Exchange on daily basis for all the countries suffering from this pandemic. In this study, three parameters logistic (autocatalytic) model is applied to characterize the disease which determine the size of epidemic with the most populated hit cases around the world respectively and predict the life cycle of COVID 19 cases by using Gaussian based prediction model. It is determined that there are worst numbers of cases of Coronavirus that are found in US and the number of CPs and RDs grow exponentially around the world underneath Spain, Italy, UK and France etc. The epicentre of this pandemic was the city of Wuhan, China. The firm defence that has been taken is to quarantine the people and the patients were cured in organized hospitals.


Background
Coronaviruses are group of viruses that infect mammals and birds. In humans these viruses produce disease through the respiratory tract and ranges from mild to lethal. In mild cases, there is common  [3]. The emergence of COVID-19 coincided with the largest annual human migration in the world, i.e., the Spring Festival travel season, which resulted in a rapid national and global spread of the virus [4]. It was primarily informed to the WHO on December 31, 2019. On January 30, 2020, the WHO acknowledged the COVID-19 outbreak a global health emergency. On March 11, 2020, the WHO declared COVID-19 a global pandemic. Illness caused by SARS-CoV-2 was recently termed COVID-19 by the WHO, the new acronym derived from "coronavirus disease 2019".

Interpretation
Covid-19 outbreak is a global disaster. There is a prodigious loss of lives, furthermore it destroy the economy of the countries worldwide as many of them have gone to the lockdown. If this pandemic has to be handled, then there is requirement of unification of the whole world to fight this disease by taking safety measures. Otherwise there is probability of great loss of human lives in this decade due to this infection as the death rate is increasing rapidly. Preparedness plans and mitigation interventions should be readied for quick deployment globally [2].

Aims
Globally, the government, doctors, paramedics, nurses, medical technicians and the community is affianced to fight with Covid-19. If we will be strong-minded and keep on struggling with this infection then there is the opportunity to triumph this conflict. In this study, we figure out the prediction of total cases of Covid-19 with each new day in those countries which have large number of cases as compared to others including US, Spain, Germany, France, Italy and China along with their death record. Ultimately, we attempt to give awareness how hazardous this pandemic could be with each new growing day and what will be the life cycle of the pandemic in terms of number of confirmed patients as well as number of reported death cases.

Methodology
In this scenario, the data is available from Humanitarian Data Exchange (HDE) of Covid-19 in each country (About 186 countries) of the world. There is the record of number of CP cases and RD cases around the world starting from January 22, 2020. Data is available for all the countries which are under the impact of this epidemic. In this study analysis for modelling is applied on US, Italy, Spain and Pakistan to evaluate and simulate for the CP and RD cases. We choose here the data up to April 28, 2020, but data is routinely updated from the HDE or other sources available online. A three parametric nonlinear logistic model is applied on the data of four most interesting countries to assess how the disease has its dynamic spread in these countries and how it will influence in near future.

Materials And Methods
In this study, we first organized the data of the countries with Covid-19 confirmed patients CP and reported deaths RD cases. The data evaluated in this study is from January 22, 2020 to April 28, 2020.
We develop model for those countries that have large number of CPs and RDs at first, so that it can be estimated that how largely this infection has its impact on the world. After that the proposed model is applied on the dataset which predict its limit of emerging infection and the deaths due to this infection on the new days in future and to estimate what will be the life cycle of the pandemic.

Proposed model used in the study
We used here three parameters nonlinear [5] logistic regression approach on the dataset. The objective of using nonlinear regression modelling is to propose a model that provides the best curve fit for the data. Then to discover parameterization (or "model function") whose Least Square estimators are as close as possible to being jointly normally distributed and unbiased, the property that prevails in a linear model [6].The nonlinear equation used in the proposed model is (see Equation

in the Supplementary Files)
Where y variable stores the size of infected people/growth rate/the number of cases in each country and x variable stores the corresponding time. The Sigmoidal behavior by modeling the current growth rate as the product of functions of the current size and remaining growth is given by: (see Equation 2 in the Supplementary Files) Where g and h are increasing functions with g(0)=h(0)=0 For many types of growth data, the growth data does not decline steadily, but rather increases to a maximum before steadily declining to zero. This is shown in the growth curve by an S-shaped, or sigmoidal pattern [6] as shown in the Figure 2. The bell-shaped curve can be used to point out growth, maximum reach point and then eventually decay rate of the disease as shown in the Figure 2.
The simplest form of equation (2) is with g (f)=h(f)=f, so that (see Equation 3 in the Supplemental

Files)
Where >0 and 0<f<A. We used κ/A for the proportionality constant so that the parameters are separately interpretable later. Thus from equation (3) the relative growth rate f -1 df/dx decreases linearly in f until f approaches A. Equation (3) has a general solution which can be written as (see Equation 4 in the Supplementary Files) This is actually the so called logistic model. The curve has asymptotes f=0 as x→ and f=A as x→ , which are, of course, never actually attained. Equation (1) is the general solution of equation (4).The parameters used in Equation (1) is also calculated as given in Table 1

Results And Discussion
As shown in the Figures 3-6, the data analysis of epidemic is given for the period Jan 22, 2020 to April 28, 2020 for US, Italy, Spain and Pakistan respectively. From the results, it is clear that the pandemic is horribly affecting the human lives with the passage of time. The model based curve which appears in red shows that how high this outbreak will be dangerous on the next incoming days. On April 28, 2020 there are 9.882e+05 infected cases of US, 1.9941e+05 cases of Italy, 2.2942e+05 cases of Spain and 13915 CPs of Pakistan. In such scenarios, there isn't a sudden fall; firstly there will be the maximum growth rate of the illness where we may see s-shape curve. Then illness will reach up to maximum growth point. Finally then illness will descent gradually. So it is important to visualize growth of the disease, its maximum reach and finally the decay.
In the Figures 7-10 statistic (Tstat) is the coefficient divided by its standard error. The standard error (SE) is an estimate of the standard deviatio coefficient, the amount it varies across cases. The p-value for each term tests the null hypothesis that the coefficient is equa (no effect). A low p-value (< 0.05) indicates that we can reject the null hypothesis. In other words, a predictor that has a low is likely to be a meaningful addition to our model because changes in the predictor's value are related to changes in the resp variable. The bell-shaped curve or Gaussian curve fitting model is applied to simulate the life cycle of the disease. It can be used to point out growth, maximum reach point and then eventually decay rate of the disease. As shown in the Figures 11-14/(Figures 15-18

Conclusion
In this study, we proposed a generalized model to analyze the epidemic of COVID-19, which was firstly reported in Wuhan last December and then quickly spread out worldwide. Our model properly     Death Analysis due to COVID-19 in Spain 28 Figure 18 Death Analysis due to COVID-19 in Pakistan

Supplementary Files
This is a list of supplementary files associated with this preprint. Click to download. Equations.pdf