Role of fractional derivatives in the mathematical modeling of the transmission of Chlamydia in the United States from 1989 to 2019

Abstract

Nowadays, the mathematical modeling of infectious diseases is a big trend worldwide. The mathematical models help us to forecast future outbreaks of diseases in the presence of present data. In this article, we represent a model of the transmission of Chlamydia in the United States by using data from 1989 to 2019. In the formulation of the model, we used integer and fractional derivatives. Several graphs are plotted for the various possible cases of the given parameters. The aim of this paper is to justify how the mathematical models in terms of fractional derivatives have more degree of freedom to explore disease dynamics for a particular data set and capture memory effects. The separate parameter estimation for each value of the fractional order increases the novelty of this work. The use of a real-data set of Chlamydia in the United States makes this study more visible and important to the literature.

Membrane computing simulation of sexually transmitted bacterial infections in hotspots of individuals with various risk behaviors

“…Recently, SIS models have incorporated stochastic networks to include asymptomatic individuals and some of the above-mentioned variables and, as in our model, personal sexual initiatives; the general conclusions are primarily consistent with ours, particularly on the benefits of diagnostic screening and protective measures ( 50 ). Other modeling studies have used non-linear fractional derivatives with the aim of projecting into the future the possible “maximum peak” of Chlamydia epidemics on the basis of cumulative available data in the United States ( 51 ). However, most of these studies do not reach the level of detail of the model presented in this work, showing the possibilities of modeling by membrane computing to allow advances and evaluate interventions in this field.…”

Is reinfection negligible effect in COVID‐19? A mathematical study on the effects of reinfection in COVID‐19

“…Here, $$$ \alpha $$$ represents the order of the fractional derivative. Due to the introduced Caputo fractional derivative, we need to redefine the parameters (to have $$$ \alpha $$$ over their powers) so that the dimension will be matched in both sides of the equation [45].…”

Feasibility and Stability Analysis for Basic Measles Model Using Fuzzy Parameter

“…The majority of research articles [26][27][28][29][30][31][32] furthermore performed some sensitivity analysis on the basis of numerous model parameters, where it was demonstrated that raising the immunization rate, boosting the effectiveness of vaccine administration, and educating the public about rubella all contribute to the control and subsequent eradication of the disease. Vellappandi et al [33,34] have derived an optimal control problem for schistosomiasis disease by using the Caputo fractional derivative. Zarin et al [35] reformulated and analyzed a co-infection model consisting of Chagas and HIV epidemics.…”