A Dynamic Study of Depression Transmission and Recovery Using Mathematical Modeling

Md. Mirajul Islam; Shafi Ahmed; Syeda Rufaida Masud; Sharmin Sultana Shanta

doi:10.53808/KUS.2026.23.01.1419-se

Authors

Md. Mirajul Islam Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh
Shafi Ahmed Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh
Syeda Rufaida Masud Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh
Sharmin Sultana Shanta Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh

DOI:

https://doi.org/10.53808/KUS.2026.23.01.1419-se

Keywords:

Mathematical model, Numerical simulation, Depressed population

Abstract

Depression has become a major global mental health issue and a significant factor contributing to suicide attempts. In this study, a nonlinear mathematical model is developed to investigate the dynamics of depression using four compartments: susceptible individuals, minor depressive disorder, major depressive disorder, and recovered individuals. The model has been analyzed qualitatively. The positivity and boundedness have been shown. The model has three equilibria: one depression-free equilibrium and two endemic equilibria for depression. Basic reproduction number is obtained, and stability analysis is performed. Sensitivity analysis to done to identify the parameters that most strongly influence the spread of depression. Numerical simulations of the model are also carried out to support the qualitative findings and demonstrate the behavior of the system. Our results reveal that the spread of depression largely depends on the progression onsets and the recovery levels. Our findings also highlight that early intervention and effective treatment strategies might be effective in reducing the prevalence of depression and its related risks.

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