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• A SEIATR compartmental model has been developed based on SEIR model and introduced to predict the 2019-nCoV. • The peak periods and peak sizes on September 16, June 13, June 29 and June 5 for India, Pakistan, Bangladesh and Afghanistan, respectively. • Basic reproduction number of currently infected cases have derived so that the defeat strategies can be imposed to control the epidemic size. A deterministic compartmental model of the corona virus diseases has been introduced to investigate the current outbreak and epidemic peaks of the 2019-nCoV in South Asian countries. We have done details analysis of the above mentioning model and demonstrated its application using publicly reported data. Based on the reported data, we have determined the new infective rate, β = 0.0017, β = 0.00069, β = 0.0011 and β = 0.00047 for India, Pakistan, Bangladesh and Afghanistan, respectively and these values are not found for other countries due to insufficient data. According to present model, the epidemic under the most restrictive measures was observed of peak on around June 29 in Bangladesh with a peak size of 4100 infectious individuals which was closed to real size of 4014. In the same way, the model results also showed that the epidemic peaks were found on around September 16 in India, June 13 in Pakistan and on June 5 in Afghanistan with the peak sizes of 97,500, 6950 and 935, respectively those were closed to the real values. In addition, we have derived a model-implied basic reproduction number for each day of currently infected cases so that the mitigation and defeat strategies can be imposed to control the size of the epidemic. [ABSTRACT FROM AUTHOR]