Fractional modelling of COVID-19 transmission incorporating asymptomatic and super-spreader individuals

TL;DR

This paper introduces a novel fractional-order compartmental model for COVID-19 that includes asymptomatic and super-spreader individuals, improving the understanding and prediction of disease transmission dynamics.

Contribution

It presents a new fractional differential equation model incorporating asymptomatic and super-spreader classes, enhancing accuracy over existing models.

Findings

Model fits real data from Portugal better than previous models.

Fractional derivatives capture memory effects in transmission dynamics.

Inclusion of super-spreaders improves model accuracy.

Abstract

The COVID-19 pandemic has presented unprecedented challenges worldwide, necessitating effective modelling approaches to understand and control its transmission dynamics. In this study, we propose a novel approach that integrates asymptomatic and super-spreader individuals in a single compartmental model. We highlight the advantages of utilizing incommensurate fractional order derivatives in ordinary differential equations, including increased flexibility in capturing disease dynamics and refined memory effects in the transmission process. We conduct a qualitative analysis of our proposed model, which involves determining the basic reproduction number and analysing the disease-free equilibrium's stability. By fitting the proposed model with real data from Portugal and comparing it with existing models, we demonstrate that the incorporation of supplementary population classes and fractional derivatives significantly improves the model's goodness of fit. Sensitivity analysis further provides valuable insights for designing effective strategies to mitigate the spread of the virus.