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This study introduces a mathematical model for disease dynamics, incorporating a non-linear incidence rate and time delay to analyze infectious disease transmission and recovery processes. Local stability is examined using the Routh-Hurwitz criterion, while global stability is established using Lyapunov functionals and the LaSalle invariance principle. The phase portraits and domain of attraction plots illustrate system dynamics, including equilibrium states, stability, intervention effects, and long-term predictions. The sensitivity analysis of R₀ with respect to the natural death rate (d) and disease-induced death rate (d₁) provides a significant contribution to their relative impact on the transmission potential of the disease. Numerical simulations support the theoretical results, providing a comprehensive and robust mathematical framework for the analysis of epidemic dynamics, with valuable insights into the stability and control of infectious diseases.
Pathak et al. (Mon,) studied this question.