Population growth model is a model that has widely been used in order to do the estimation and forecasting the population of peoples, animals, bacteria and even in economics growth. Many studies have been carried out by the researchers on population growth model by considering the factors of birth, death and carrying capacity in order to predict the number of population at certain area. From previous the studies there was only one study that involved the factor of migration as an input in the logistic model. The value of the migration is a constant value. Therefore in contrast with the above modified logistic model, in this study logistic model is modified by adding a migration factor as a function of population. This function takes into account the migration and the interaction between peoples that is limited to the carrying capacity of the environment. This model can be solved qualitatively by using the analysis of equilibrium point and quantitatively by using the separable variables method. Both of these methods produce the same result. Modified logistic model has been applied in the population data of Purwanegara village in Jawa Tengah Province, Indonesia. By using the data, through the graph method and analysis of equilibrium point the same results are produced, where for the long term behavior the population of Purwanegara village will approach to the maximum value of 68,495 persons. Modified logistic model gives average absolute error percentage which is 0.61376782 % for the estimation of the population from January, 2012 until October, 2016. Then, based on validation model, the absolute error percentage which is 2.79737591 % for the estimation of the population in November, 2016. Hence, based on the graph method, prediction for the population in Purwanegara village from December 2016 until December 2018 can be done. From the results, the modified logistic model with migration factor as a function of population gives a better result for predicting the population of Purwanegara village in Jawa Tengah Province, Indonesia compared to logistic model
