Transmission dynamics of depression in socially connected population: A nonlinear modeling study

Abstract

Human emotions are considered to be contagious that can be transmitted from one person to another during social interactions. However, interaction with people having excessive negative emotions may make other people depressed. Taking this aspect into consideration, a SIR nonlinear model is formulated to investigate the transmission dynamics of depression in social connections. Through qualitative analysis of the model, critical value of depression is determined. Two equilibria, viz. depression free and depression state, are obtained and their stability behaviors are analyzed. The stability analysis reveals the fact that both the equilibria are locally and globally stable, depending on critical value of depression. The sensitivity analysis of crucial parameters of critical value of depression is performed to point out the key parameters that can drastically influence the propagation of depression. The results demonstrate the importance of counselling for depressed persons in order to suppress the growth of depression in social connections. The model calibration has been done for the annual depression cases of Zimbabwe. The results of our study show that individuals will catch major depression disorders more quickly once they get initially (primary) depressed. For this, counselling rate for primary depressed population should be increased.