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 C 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.

The aim of this paper is to show how North Cyprus fought with Covid-19 by using R0 and Rt, as herd immunity. For that purpose, we used a SEIR model for basic reproduction number, R0, and calculated Rt values by using R0 values. North Cyprus is the first country in Europe to free from Covid-19 epidemic. One of the most important reasons for this is that the government decided to tackle Covid-19 pandemic by using R0 and Rt daily. For R0, we constructed a new SEIR model by using real data for North Cyprus. From March 11, 2020 to May 15, 2020, R0 varies from 0.65 to 2.38.

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-β) 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.

Breast Imaging Reporting and Data System, also known as BI-RADS is a universal system used by radiologists and doctors. It constructs a comprehensive language for the diagnosis of breast cancer. BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories. Mathematical models play an important role in the diagnosis and treatment of cancer. In this study, data of 42 BI-RADS 4 patients taken from the Center for Breast Health, Near East University Hospital is utilized. Regarding the analysis, a mathematical model is constructed by dividing the population into 4 compartments. Sensitivity analysis is applied to the parameters with the desired outcome of a reduced range of cancer risk. Numerical simulations of the parameters are demonstrated. The results of the model have revealed that an increase in the lactation rate and early menopause have a negative correlation with the chance of being diagnosed with BI-RADS 4 whereas a positive correlation increase in age, the palpable mass, and family history is distinctive. Furthermore, the negative effects of smoking and late menopause on BI-RADS 4C diagnosis are vehemently outlined. Consequently, the model showed that the percentages of parameters play an important role in the diagnosis of BI-RADS 4 subcategories. All things considered, with the assistance of the most effective parameters, the range of cancer risks in BI-RADS 4 subcategories will decrease.

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