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September 10, 2025

Application of nonlinear stochastic fractional systems in the generalized SEIR model

HTHengameh TamimiIran University of Science and Technology RSReza SaadatiIran University of Science and Technology MGMohammad Bagher GhaemiIran University of Science and Technology

Key Points

The generalized SEIR model accounts for random disease transmission, enhancing traditional understanding.
The model improves predictions during seasonal illnesses, indicating potential spikes in transmission rates.
Employing a measure of noncompactness ensures the existence of solutions within the model’s parameters.
A novel numerical method is introduced to analyze and validate practical examples of the proposed model.

Abstract

In this article, we successfully generalize the SEIR (Susceptible, Exposed, Infected, and Recovered) model to account for random and intermittent instances of disease transmission. This model explains the increased probability of disease transmission during specific periods, particularly for seasonal illnesses. Furthermore, we investigate the conditions necessary to ensure at least one solution for this model by employing the measure of noncompactness. Following this, we introduce a new approach that examines convergence, after which we apply the proposed numerical method to study practical examples.

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