DIABETES MELLITUS WITH CO-INFECTION OF COVID-19 VIRUS BY USING FRACTAL FRACTIONAL OPERATOR

Abstract

COVJD-19 is linked to diabetes, increasing the likelihood and severity of outcomes due to hyperglycaemia, immune system impaim1ent, vaswlar problems, and comorbidities like hypertension, obesity, and cardiovascular disease, which can lead to catastrophic outcomes. The study presents a novel COVID-19 management approach for diabetic patients using a fractal fractional operator and Mittag-Leffler kemel. It uses the Lipschitz criterion and linear growth to identify the solution singularity and analyses the global derivative impact, confi1111ing unique solutions and demonstrating 'the bounded nature of the proposed system. The study examines the impact of COVID-19 on individuals with diabetes, using global stability analysis and quantitative examination of equilibrium states. Sensitivity analysis is conducted using reproductive numbers to dete1111ine the disease's status in society and the impact of control strategies, highlighting the importance of understanding epidemic problems and their properties. This study uses two-step Lagrange polynomial to analyze the impact of the fractional operator on a proposed model. Numerical simulations using MA TLAB validate the effects of COVID-19 on diabetic patients and allow predictions based on the established theoretical framework, supporting the theoretical findings. This study will help to observe and understand how COVJD-19 affects-people with diabetes. This will help with control plans in the future to lessen the effects of COVID-19.

Specification

PREAMBLE TO THE DESCRIPTION
THE FIELD OF INVENTION
The field of invention relates to mathematical modeling and numerical analysis,
specifically within the context of epidemiological studies of infectious diseases like
COVID-19 in populations with underlying health conditions such as diabetes. The
invention involves the use of fractal fractional operators to improve the accuracy and
reliability of these models.
BACKGROUND OF THE INVENTION
The invention addresses the need for more accurate models to predict the spread and impact
of COVID-19, particularly among individuals with diabetes, who are at higher risk of
.severe outcomes. Traditional mathematical models often fail to capture the complexities of
real-world data, especially when dealing with comorbidities like diabetes. The use of fractal
fractional operators, which combine fractional calculus and fractal geometry, allows for a
more nuanced approach, improving the representation of memory effects and the dynamics
of disease spread in these populations.
SUMMARY OF THE INVENTION
The invention proposes a novel COVID-19 management approach for diabetic patients by
incorporating a fractal fractional operator with a Mittag-Leffler kernel into the
epidemiological model. This approach allows for the identification of unique solutions,
stability analysis, and predictions of disease dynamics. The model is validated using
numerical simulations with MA TLAB, which supports its effectiveness in predicting the
impact of COVID-19 on diabetic patients. The study highlights the importance of
understanding the properties of epidemic problems and suggests that this advanced modeling
approach can help develop better control strategies for future pandemics.




COMPLETE SPECIFICATION
Specifications
o Focus: The invention belongs to the field of mathematical modeling and
numerical analysis, specifically within the context of epidemiology, applied to the
study of infectious diseases like COVI0-19, especially in populations with
comorbidities such as diabetes.
o Numerical Simulation: The invention is validated through numerical simulations
using MA TLAB, which demonstrates the impact of COVI0-19 on diabetic
patients under various scenarios, including different fractional orders.
o Incorporation of Fractional Calculus: The invention utilizes a fractal fractional
operator, which combines elements of fractional. calculus and fractal geometrY, to
model the memorY effects and complex dynamics of disease spread. The operator
is defined in the Riemann-Liouville sense with specific order parameters.


DESCRIPTION
• Objective: The primary objective of this invention is to develop a more accurate and reliable
mathematical model to study the dynamics of COVID-19 infection in populations with underlying
conditions, specifically diabetes mellitus. Traditional models often fall short in capturing the intricate
interactions between COVID-19 and diabetes, which can lead to significant differences in disease
outcomes.
• Novel Perspective: This novel perspective advances the field of epidemiological modeling, offering a
powerful tool for managing and understanding the complex dynamics of COVID-19 in diabetic
populations.



CLAIM
I. Enhanced Understanding: This operator is a sophisticated mathematical tool that combines
the principles of fractional calculus with fractal geometry. Unlike standard operators, it allows
for the modeling of systems with memory effects and complex, non-linear dynamics. This is
particularly useful for capturing the long-term interactions between COVID-19 and chronic
conditions like diabetes.
2. Improved Prediction: Improve the accuracy of predictions related to the spread and impact
of COVID-19 among diabetic patients. Analyze and predict the stability and behavior of the
epidemic under various conditions, such as different levels of fractional order in the
mathematical model. Provide a tool for public health officials to better understand and
manage the risks associated with co-infections like COVID-19 in vulnerable populations.
3. Integrated Disease Modelling: The invention does not just apply these mathematical
techniques in isolation but integrates them into a comprehensive model that accounts for the
unique interactions berween diabetes and COVID-19. This results in a model that more
accurately reflects the real-world dynamics of disease transmission and progression in
populations with comorbidities.
4. Enhanced Predictive Capabilities: By utilizing this novel approach, the model provides better
predictive capabilities, particularly in understanding the outcomes of public health
interventions and control strategies in diabetic populations. It allows for more nuanced
predictions that can inform targeied interventions to reduce mortality and severe outcomes in
these high-risk groups

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