An analysis of the Caputo Fabrizio fractional modeling for infectious diseases caused by chlamydia

Ali Hasan; Muhammad Azeem; Sana Ullah Saqib Ullah Saqib; Muhammad Manan Akram

doi:10.48165/jmmfc.2024.1206

Authors

Ali Hasan Department of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan.
Muhammad Azeem Department of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan.
Sana Ullah Saqib Ullah Saqib Department of Applied Mathematics, National Chung Hsing University, Taichung, Taiwan.
Muhammad Manan Akram Washington university of Science and Technology ,USA.

DOI:

https://doi.org/10.48165/jmmfc.2024.1206

Keywords:

Chlamydia Model, Existence, Unicity and stability, Numerical scheme

Abstract

These days, infectious illness mathematical modeling is a major global trend. With the use of current data, mathematical models enable us to predict the occurrence of disease outbreaks in the future. In this work, we use a fractal fractional operator with two fractal and fractional orders to solve a system of fractional differential equations using a Caputo Fabrizio type kernel. A six chambered model with a single source of chlamydia is studied using the concept of fractal fractional derivatives with nonsingular and nonlocal fading memory. The fractal fractional model of the Chlamydia system can be solved by using the characteristics of a non-decreasing and compact mapping. Initially, we calculate the system’s equilibrium points and fundamental reproduction number R0. We then look at the system’s stability at the equilibrium point. Through the application of the Picard Lindelof methodology, we establish the existence of a unique solution for the given fractional CF-system of the hearing loss model and use fixed point theory to examine the stability of the iterative process. By taking into account the therapy as a control technique to lower the number of infected individuals, the system’s optimal control is established. Calculating the estimated solution of the system involves applying the Euler technique for the fractional order Caputo Fabrizio derivative. In two scenarios, R0 < 1 and R0 > 1, we provide a numerical simulation of the disease’s spread with regard to the basic reproduction number and the transmission rate. We compute the results for various fractional order derivatives and compare the findings in order to examine the impact of the fractional order derivative on the behavior and value of each variable in the model. Additionally, we examine the sensitivity of R0 with regard to each model parameter and ascertain the influence of each parameter, taking into account the significance of reproduction number in the persistence of disease transmission. Finally, it can be said that once more, fractional operator mathematical models can help in making better decisions on how to manage financially turbulent situations.

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