  We propose a mathematical model to analyze the time evolution of the total
number of infected population with Covid-19 disease at a region in the ongoing
pandemic. Using the available data of Covid-19 infected population on various
countries we formulate a model which can successfully track the time evolution
from early days to the saturation period in a given wave of this infectious
disease. It involves a set of effective parameters which can be extracted from
the available data. Using those parameters the future trajectories of the
disease spread can also be projected. A set of differential equations is also
proposed whose solutions are these time evolution trajectories. Using such a
formalism we project the future time evolution trajectories of infection spread
for a number of countries where the Covid-19 infection is still rapidly rising.
