Dynamical analysis of novel minimal SEIR model incorporating asymptomatic transmission

Patel, Viralkumar D.; Hasmani, Abdulvahid H.

doi:10.22124/jmm.2025.31474.2832

Dynamical analysis of novel minimal SEIR model incorporating asymptomatic transmission

Articles in Press

Document Type : Research Article

Authors

¹ Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat, India. Department of Mathematics, Shri Alpesh N. Patel Post Graduate Institute of Science & Research, Anand.

² Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, India.

10.22124/jmm.2025.31474.2832

Abstract

We propose a modified SEIR model that includes asymptomatic transmission directly in the infection term, avoiding the need for a separate asymptomatic compartment while keeping the model realistic. The basic reproduction number ($\mathcal{R}_0$) is calculated to measure the potential for disease spread. Local stability analysis shows that the disease-free equilibrium is stable when $\mathcal{R}_0 < 1$ and unstable when $\mathcal{R}_0 > 1$, while the endemic equilibrium is locally stable in the latter case. A forward bifurcation at $\mathcal{R}_0 = 1$ is identified, indicating a smooth transition from the disease-free equilibrium to a unique endemic equilibrium without coexistence of the two equilibria. Global stability results show that the disease-free state is globally asymptotically stable for $\mathcal{R}_0 \leq 1$, and the endemic state is globally asymptotically stable for $\mathcal{R}_0 > 1$. Simulations using early COVID‑19 data support these findings, showing that higher asymptomatic transmission prolongs outbreaks, increases peaks, and delays elimination. Evaluation of control strategies reveals that isolation is more effective than testing alone, and their combination produces the greatest overall reduction in disease spread under appropriate assumptions.

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