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

Role of fractional derivatives in pharmacokinetic/pharmacodynamic anesthesia model using BIS data

In this paper, we investigate a pharmacokinetic/pharmacodynamic model for anesthesia to describe the effects of propofol and the impact of fractional derivatives. Using actual bispectral index data from surgical patients, we demonstrate how fractional-order models can more effectively capture the memory-dependent dynamics of anesthesia than traditional integer-order models. Model parameters are estimated using the trust region reflective algorithm, and numerical simulations employ the Adams-type predictor-corrector method. Comparative analysis across multiple patients reveals that the fractional-order model consistently provides a superior fit to bispectral index data, as indicated by lower prediction errors and reduced Akaike information criterion values. This study primarily aims to demonstrate the advantages of employing fractional derivatives for this specific data set, particularly in accounting for memory effects, which are crucial in capturing the prolonged effects of anesthetic agents. By incorporating actual bispectral index scale data and fractional derivatives, we significantly enhance the relevance and impact of this research, offering a more flexible and accurate model. Our findings highlight the superiority of fractional derivatives in capturing the complex, time-dependent dynamics of anesthetic drug effects, making it a more suitable modeling approach compared to traditional methods, with the potential for improved patient-specific anesthesia management.

Mathematical analysis of fractional Chlamydia pandemic model

In this study, we developed a Caputo-Fractional Chlamydia pandemic model to describe the disease's spread. We demonstrated the model's positivity and boundedness, ensuring biological relevance. The existence and uniqueness of the model's solution were established, and we investigated the stability of the α-fractional order model. Our analysis proved that the disease-free equilibrium point is locally asymptotically stable. Additionally, we showed that the model has a single endemic equilibrium point, which is globally asymptotically stable when [Formula: see text] exceeds 1. Using Latin Hypercube sampling and partial rank correlation coefficients (PRCCs), sensitivity analysis identified key parameters influencing [Formula: see text]. Numerical simulations further illustrated the impact of parameter variations on disease dynamics.

Chlamydia infection with vaccination asymptotic for qualitative and chaotic analysis using the generalized fractal fractional operator

In this work, we solve a system of fractional differential equations utilizing a Mittag-Leffler type kernel through a fractal fractional operator with two fractal and fractional orders. A six-chamber 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. A suggested model with the Lipschitz criteria and linear growth is studied both qualitatively and quantitatively, taking into account boundedness, uniqueness, and positive solutions at equilibrium points with Leray-Schauder results under time scale concepts. We examined the framework of local and global stability and insight into Lyapunov function properties for the infectious disease model. Chaos Control will employ the regulate for linear responses approach to stabilize the system following its equilibrium points. This will take into consideration a fractional order framework with a managed design, where solutions are bounded in the feasible domain and have a greater impact at the lower minimum infectious rate. To illustrate the implications of fractional and fractal dimensions with varying interest rate values through simulations with Newton's polynomial method under the Mittag-Lefller kernel. Additionally, a comparative analysis of results is also derived by employing power and exponential decay kernels at various fractional orders.

A decade of thermostatted kinetic theory models for complex active matter living systems

In the last decade, the thermostatted kinetic theory has been proposed as a general paradigm for the modeling of complex systems of the active matter and, in particular, in biology. Homogeneous and inhomogeneous frameworks of the thermostatted kinetic theory have been employed for modeling phenomena that are the result of interactions among the elements, called active particles, composing the system. Functional subsystems contain heterogeneous active particles that are able to perform the same task, called activity. Active matter living systems usually operate out-of-equilibrium; accordingly, a mathematical thermostat is introduced in order to regulate the fluctuations of the activity of particles. The time evolution of the functional subsystems is obtained by introducing the conservative and the nonconservative interactions which represent activity-transition, natural birth/death, induced proliferation/destruction, and mutation of the active particles. This review paper is divided in two parts: In the first part the review deals with the mathematical frameworks of the thermostatted kinetic theory that can be found in the literature of the last decade and a unified approach is proposed; the second part of the review is devoted to the specific mathematical models derived within the thermostatted kinetic theory presented in the last decade for complex biological systems, such as wound healing diseases, the recognition process and the learning dynamics of the human immune system, the hiding-learning dynamics and the immunoediting process occurring during the cancer-immune system competition. Future research perspectives are discussed from the theoretical and application viewpoints, which suggest the important interplay among the different scholars of the applied sciences and the desire of a multidisciplinary approach or rather a theory for the modeling of every active matter system.

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

The epidemiology of sexually transmitted infections (STIs) is complex due to the coexistence of various pathogens, the variety of transmission modes derived from sexual orientations and behaviors at different ages and genders, and sexual contact hotspots resulting in network transmission. There is also a growing proportion of recreational drug users engaged in high-risk sexual activities, as well as pharmacological self-protection routines fostering non-condom practices. The frequency of asymptomatic patients makes it difficult to develop a comprehensive approach to STI epidemiology. Modeling approaches are required to deal with such complexity. Membrane computing is a natural computing methodology for the virtual reproduction of epidemics under the influence of deterministic and stochastic events with an unprecedented level of granularity. The application of the LOIMOS program to STI epidemiology illustrates the possibility of using it to shape appropriate interventions. Under the conditions of our basic landscape, including sexual hotspots of individuals with various risk behaviors, an increase in condom use reduces STIs in a larger proportion of heterosexuals than in same-gender sexual contacts and is much more efficient for reducing Neisseria gonorrhoeae than Chlamydia and lymphogranuloma venereum infections. Amelioration from diagnostic STI screening could be instrumental in reducing N. gonorrhoeae infections, particularly in men having sex with men (MSM), and Chlamydia trachomatis infections in the heterosexual population; however, screening was less effective in decreasing lymphogranuloma venereum infections in MSM. The influence of STI epidemiology of sexual contacts between different age groups (<35 and ≥35 years) and in bisexual populations was also submitted for simulation.IMPORTANCEThe epidemiology of sexually transmitted infections (STIs) is complex and significantly influences sexual and reproductive health worldwide. Gender, age, sexual orientation, sexual behavior (including recreational drug use and physical and pharmacological protection practices), the structure of sexual contact networks, and the limited application or efficiency of diagnostic screening procedures create variable landscapes in different countries. Modeling techniques are required to deal with such complexity. We propose the use of a simulation technology based on membrane computing, mimicking in silico STI epidemics under various local conditions with an unprecedented level of detail. This approach allows us to evaluate the relative weight of the various epidemic drivers in various populations at risk and the possible outcomes of interventions in particular epidemiological landscapes.