COVID-19 or SARS-Cov-2, affecting 6 million people and more than 300,000 deaths, the global pandemic has engulfed more than 90% countries of the world. The virus started from a single organism and is escalating at a rate of 3% to 5% daily and seems to be a never ending process. Understanding the basic dynamics and presenting new predictions models for evaluating the potential effect of the virus is highly crucial. In present work, an evolutionary data analytics method called as Genetic programming (GP) is used to mathematically model the potential effect of coronavirus in 15 most affected countries of the world. Two datasets namely confirmed cases (CC) and death cases (DC) were taken into consideration to estimate, how transmission varied in these countries between January 2020 and May 2020. Further, a percentage rise in the number of daily cases is also shown till 8 June 2020 and it is expected that Brazil will have the maximum rise in CC and USA have the most DC. Also, prediction of number of new CC and DC cases for every one million people in each of these countries is presented. The proposed model predicted that the transmission of COVID-19 in China is declining since late March 2020; in Singapore, France, Italy, Germany and Spain the curve has stagnated; in case of Canada, South Africa, Iran and Turkey the number of cases are rising slowly; whereas for USA, UK, Brazil, Russia and Mexico the rate of increase is very high and control measures need to be taken to stop the chains of transmission. Apart from that, the proposed prediction models are simple mathematical equations and future predictions can be drawn from these general equations. From the experimental results and statistical validation, it can be said that the proposed models use simple linkage functions and provide highly reliable results for time series prediction of COVID-19 in these countries.