Cancer is a noncommunicable chronic disease that indistinctly affects people of any nationality, race, ethnicity, age, or social class. Because of its unpredictability, receiving the diagnosis of this disease is almost always alarming for the patient. Breast cancer, especially among women, occupies a prominent position in this ranking. However, if diagnosed early, there is an excellent chance of a cure. In this sense, digital technologies have been advancing at an increasingly fast pace to support the early diagnosis of the disease. Clinical analysis of breast cancer is commonly performed using diagnostic imaging. One of the most used exams considered the main one for the early detection of this type of cancer is mammography. This exam allows the visualization of breast tissue from image screening using X-rays. In this sense, the use of computational techniques is essential to assist medical professionals in diagnosing this disease, thus making prevention and early diagnosis even more effective in the current context. The present work is limited to the use of digital technologies (image processing and artificial intelligence) that cooperate with the early diagnosis of breast cancer, which supports the medical professional to analyze images and be able to diagnose, from an early stage, the emergence of breast cancer of the disease, significantly increasing the chances of curing it. It can be gathered from this research how the discovery of X-rays and the growth in this sector combined with cutting-edge technology have benefitted in the early detection of the disease and even offered the cure of many cases.

This paper presents a novel idea as it investigates the rescue effect of the prey with fluctuation effect for the first time to propose a modified predator-prey model that forms a non-autonomous model. However, the approximation method is utilized to convert the non-autonomous model to an autonomous one by simplifying the mathematical analysis and following the dynamical behaviors. Some theoretical properties of the proposed autonomous model like the boundedness, stability, and Kolmogorov conditions are studied. This paper's analytical results demonstrate that the dynamic behaviors are globally stable and that the rescue effect improves the likelihood of coexistence compared to when there is no rescue impact. Furthermore, numerical simulations are carried out to demonstrate the impact of the fluctuation rescue effect on the dynamics of the non-autonomous model. The analytical and numerical results show a more coexisted model between prey and predator, which can help any extinction-threatened ecosystem.