Dynamics and Stability Analysis of COVID-19 Using SEAIHR Epidemic Model with Sensitivity and Numerical Investigation

Abstract

This study develops and analyzes a modified SEAIHR (Susceptible–Exposed–Asymptomatic–Infectious–Hospitalized–Recovered) epidemic model to investigate the transmission dynamics of COVID-19 in India. The model incorporates awareness, self-monitoring, and hospitalization effects to reflect behavioral adaptation and clinical transitions within the population. Mathematical properties such as positivity, boundedness, and the existence of equilibrium points are established to ensure biological feasibility. The basic reproduction number, derived using the next-generation matrix approach, is obtained as R_o=2.5307 , indicating that the infection can persist under baseline conditions. Local and global stability analyses are performed for both disease-free and endemic equilibria using the Routh–Hurwitz and Lyapunov methods. Sensitivity (elasticity) analysis of R_o reveals that the transmission coefficient (α)  the progression fraction to symptomatic infection (θ_i)  , and the infectiousness coefficient of symptomatic individuals (e₂) are the most influential parameters enhancing disease spread. In contrast, removal and hospitalization rates  exhibit negative elasticities, signifying their effectiveness in disease control. Numerical simulations based on the classical fourth-order Runge–Kutta (RK4) method with a fixed time step of    day validate the analytical findings. The time-series trajectories show typical epidemic peaks with convergence to a stable endemic equilibrium for R₀>1 , while phase-plane plots confirm global asymptotic stability. The results emphasize that early detection, isolation, and improved hospitalization efficiency can substantially mitigate COVID-19 transmission and ensure long-term disease control in India.