Author(s)

Ifeoma D. Omoko^1*, Oluwabusayo Oni², Taiwo G. Alabi³, Muritala B. Taoreed⁴

¹Department of Mathematics, Lagos State University, Ojo, Lagos, Nigeria.
²Department of Mathematics, Oregon State University, Oregon, USA.
³Department of Mathematics, University of Tennessee, USA.
⁴Department of Mathematics, Boise State University, Boise, Idaho, USA.

This study examines the construction of Intrinsic Lyapunov functions to investigate the asymptotic stability of equilibrium states analyzed under specific conditions involving interaction coefficients and compartmental transitions. It involves the qualitative properties of stratified compartmental models for drug user populations within heterogeneous communities using intrinsic Lyapunov methods. These models categorize populations into different compartments (e.g., susceptible individuals, drug users, and those undergoing treatment) and account for interactions among these subpopulations. The system is governed by nonlinear ordinary differential equations, with parameters representing initiation, recovery, and relapse rates. Additionally, the boundedness of solutions is established, ensuring that population variables (e.g. the number of drug users) remain within biologically feasible limits over a period of time. These findings provide theoretical insights into the long-term dynamics of drug user populations, highlighting the impact of prevention, treatment, and socio-environmental factors. The results underscore the effectiveness of intrinsic Lyapunov methods in understanding stratified population dynamics and guiding targeted intervention strategies to control drug prevalence.

Nonlinear Differential Equations, Stability, Boundedness, Intrinsic Lyapunov Method, Population Models

Omoko, I. , Oni, O. , Alabi, T. and Taoreed, M. (2025) Dynamical Models in Intrinsic Lyapunov Methods. Journal of Applied Mathematics and Physics, 13, 1352-1364. doi: 10.4236/jamp.2025.134073.