On a Symmetry-Based Structural Deterministic Fractal Fractional Order Mathematical Model to Investigate Conjunctivitis Adenovirus Disease

• Published in: Symmetry (Basel) Vol. 16; no. 10; p. 1284
• Main Authors: Jeelani, Mdi Begum, Alharthi, Nadiyah Hussain
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-10-2024
• Subjects: Adenoviruses; Analysis; biological model of conjunctivitis adenovirus disease; Biological models (mathematics); Biology; Calculus; Conjunctivitis; Demographics; Diseases; Dynamic structural analysis; Epidemiology; Eye diseases; Fixed points (mathematics); Fractal analysis; fractal fractional order derivative; Fractal models; Fractals; Fractional calculus; Functional analysis; Health aspects; Impact analysis; Infections; Infectious diseases; Investigations; Mathematical analysis; Mathematical models; Mathematicians; Mathematics; Medical research; Medicine, Experimental; Numerical analysis; Numerical methods; numerical solution; Qualitative analysis; qualitative theory; Researchers; Sensitivity analysis; Viruses
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym16101284

In the last few years, the conjunctivitis adenovirus disease has been investigated by using the concept of mathematical models. Hence, researchers have presented some mathematical models of the mentioned disease by using classical and fractional order derivatives. A complementary method involves analyzing the system of fractal fractional order equations by considering the set of symmetries of its solutions. By characterizing structures that relate to the fundamental dynamics of biological systems, symmetries offer a potent notion for the creation of mechanistic models. This study investigates a novel mathematical model for conjunctivitis adenovirus disease. Conjunctivitis is an infection in the eye that is caused by adenovirus, also known as pink eye disease. Adenovirus is a common virus that affects the eye’s mucosa. Infectious conjunctivitis is most common eye disease on the planet, impacting individuals across all age groups and demographics. We have formulated a model to investigate the transmission of the aforesaid disease and the impact of vaccination on its dynamics. Also, using mathematical analysis, the percentage of a population which needs vaccination to prevent the spreading of the mentioned disease can be investigated. Fractal fractional derivatives have been widely used in the last few years to study different infectious disease models. Hence, being inspired by the importance of fractal fractional theory to investigate the mentioned human eye-related disease, we derived some adequate results for the above model, including equilibrium points, reproductive number, and sensitivity analysis. Furthermore, by utilizing fixed point theory and numerical techniques, adequate requirements were established for the existence theory, Ulam–Hyers stability, and approximate solutions. We used nonlinear functional analysis and fixed point theory for the qualitative theory. We have graphically simulated the outcomes for several fractal fractional order levels using the numerical method.