Exponential growths are observed in several natural phenomena, including cosmological expansion of the universe, nuclear fission, population growth, global viral spread, and financial markets fluctuations. Several deterministic and stochastic methods have been used for the modeling of dynamics of these phenomena. Global reliable data are essential to parameterise a defined model so as to enhance confidence in model outputs. Four-parameter logistic model comes out to be best forecast model for the total Covid-19 infected people in Pakistan and India. Five-parameter logistic model is best forecast model for Bangladesh. Simulation results revel that maximum total number of cases will be about 1.0, 0.6 and 0.25 million in India, Pakistan and Bangladesh respectively. Covid-19 infected rate will be closed to 11000, 8000 and 2000 cases per day during peak period in these countries.