Epidemic Transmission Modeling with Fractional Derivatives and Environmental Pathogens

TL;DR

This paper introduces a fractional-order compartmental model for COVID-19 that incorporates environmental pathogen effects, capturing memory effects and providing insights into transmission dynamics and control strategies.

Contribution

It develops a novel fractional calculus-based model that includes environmental shedding, offering a more comprehensive understanding of COVID-19 transmission compared to classical models.

Findings

Model accurately fits real COVID-19 data

Environmental transmission significantly impacts disease spread

Fractional derivatives capture memory effects in transmission dynamics

Abstract

This research presents an advanced fractional-order compartmental model designed to delve into the complexities of COVID-19 transmission dynamics, specifically accounting for the influence of environmental pathogens on disease spread. By enhancing the classical compartmental framework, our model distinctively incorporates the effects of order derivatives and environmental shedding mechanisms on the basic reproduction numbers, thus offering a holistic perspective on transmission dynamics. Leveraging fractional calculus, the model adeptly captures the memory effect associated with disease spread, providing an authentic depiction of the virus's real-world propagation patterns. A thorough mathematical analysis confirming the existence, uniqueness, and stability of the model's solutions emphasizes its robustness. Furthermore, the numerical simulations, meticulously calibrated with real COVID-19 case data, affirm the model's capacity to emulate observed transmission trends, demonstrating the pivotal role of environmental transmission vectors in shaping public health strategies. The study highlights the critical role of environmental sanitation and targeted interventions in controlling the pandemic's spread, suggesting new insights for research and policy-making in infectious disease management.