A fractional-order model for nosocomial infection caused by Pseudomonas aeruginosa in Northern Cyprus.

Pseudomonas aeruginosa, a resilient gram-negative bacterium, poses a persistent threat as a leading cause of nosocomial infections, particularly in resource-constrained regions. Despite existing treatment and control measures, the bacterium continues to challenge healthcare systems, especially in developing nations. This paper introduces a fractional-order model to elucidate the dynamic behavior of nosocomial infections caused by P. aeruginosa and to compare the efficacy of carbapenems and aminoglycosides in treatment. The model's existence and uniqueness are established, and both global and local stability are confirmed. The effective reproduction number is computed, revealing an epidemic potential with a value of 1.02 in Northern Cyprus. Utilizing real-life data from a university hospital and employing numerical simulations, our results indicate that patients exhibit higher sensitivity and lower resistance to aminoglycoside treatment compared to carbapenems. Aminoglycosides consistently outperform carbapenems across key metrics, including the reduction of susceptible population, infection numbers, treatment efficacy, total infected population, hospital occupancy, and effective reproduction number. The fractional-order approach emerges as a suitable and insightful tool for studying the transmission dynamics of the disease and assessing treatment effectiveness. This research provides a robust foundation for refining treatment strategies against P. aeruginosa infections, contributing valuable insights for healthcare practitioners and policymakers alike.

A fractional-order mathematical model for lung cancer incorporating integrated therapeutic approaches.

This paper addresses the dynamics of lung cancer by employing a fractional-order mathematical model that investigates the combined therapy of surgery and immunotherapy. The significance of this study lies in its exploration of the effects of surgery and immunotherapy on tumor growth rate and the immune response to cancer cells. To optimize the treatment dosage based on tumor response, a feedback control system is designed using control theory, and Pontryagin's Maximum Principle is utilized to derive the necessary conditions for optimality. The results reveal that the reproduction number [Formula: see text] is 2.6, indicating that a lung cancer cell would generate 2.6 new cancer cells during its lifetime. The reproduction coefficient [Formula: see text] is 0.22, signifying that cancer cells divide at a rate that is 0.22 times that of normal cells. The simulations demonstrate that the combined therapy approach yields significantly improved patient outcomes compared to either treatment alone. Furthermore, the analysis highlights the sensitivity of the steady-state solution to variations in [Formula: see text] (the rate of division of cancer stem cells) and [Formula: see text] (the rate of differentiation of cancer stem cells into progenitor cells). This research offers clinicians a valuable tool for developing personalized treatment plans for lung cancer patients, incorporating individual patient factors and tumor characteristics. The novelty of this work lies in its integration of surgery, immunotherapy, and control theory, extending beyond previous efforts in the literature.

Crank-Nicholson difference scheme for the system of nonlinear parabolic equations observing epidemic models with general nonlinear incidence rate.

In this work, we study second order Crank-Nicholson difference scheme (DS) for the approximate solution of problem (1). The existence and uniqueness of the theorem on a bounded solution of Crank-Nicholson DS uniformly with respect to time step τ is proved. In practice, theoretical results are presented on four systems of nonlinear parabolic equations to explain how it works on one and multidimensional problems. Numerical results are provided.

Dynamics of HIV/AIDS in Turkey from 1985 to 2016.

In this paper, we formulated a mathematical model that studies the dynamics of HIV/AIDS in Turkey from 1985 to 2016. We find two equilibrium points, disease free equilibrium and endemic equilibrium. Global stability analysis of the equilibria was conducted using Lyapunov function which depends on the basic reproduction ratio R 0. If R 0 < 1, the disease free equilibrium point is globally asymptotically stable, and if R 0 ≥ 1 the endemic equilibrium point is globally asymptotically stable. We computed and predicted the basic reproduction ratios across all the years. It was found out that there were flaws in the exact values of R 0 which is related to the poor registration system of HIV/AIDS in Turkey. Hence, there is need for the government to improve the system in order to cover the actual cases of the disease. The increase of the basic reproduction ratio over the years also shows the need for the relevant authorities to adopt appropriate control measures in combating the disease.

Dynamics of Immune Checkpoints, Immune System, and BCG in the Treatment of Superficial Bladder Cancer.

This paper aims to study the dynamics of immune suppressors/checkpoints, immune system, and BCG in the treatment of superficial bladder cancer. Programmed cell death protein-1 (PD-1), cytotoxic T-lymphocyte-associated antigen 4 (CTLA4), and transforming growth factor-beta (TGF-ß) are some of the examples of immune suppressors/checkpoints. They are responsible for deactivating the immune system and enhancing immunological tolerance. Moreover, they categorically downregulate and suppress the immune system by preventing and blocking the activation of T-cells, which in turn decreases autoimmunity and enhances self-tolerance. In cancer immunotherapy, the immune checkpoints/suppressors prevent and block the immune cells from attacking, spreading, and killing the cancer cells, which leads to cancer growth and development. We formulate a mathematical model that studies three possible dynamics of the treatment and establish the effects of the immune checkpoints on the immune system and the treatment at large. Although the effect cannot be seen explicitly in the analysis of the model, we show it by numerical simulations.