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Cancer is a very challenging issue in terms of people’s health and lives around the world. Cancer refers to a collection of illnesses distinguished by the formation of tumour cells, malignant cells, or cancer cells that have the potential to become cancerous. Millions of people across the globe are suffering from this illness. Several studies on cancer and related diseases have been made in recent years. The main goal of this article is to computationally examine the tumour–immune–vitamins (TIV) system dynamics, which incorporates the effect of vitamin intervention on enhancing the immune system and its aspects on squeezing and delaying tumour cell production and division. We analyse the model with different fractional approaches to learn more about its dynamics. Initially, the TIV model is proposed with Caputo–Fabrizio (CF) derivative. We investigate the existence and uniqueness of the solutions of the suggested fractional model using fixed-point results. Furthermore, we modify the TIV system with conformable and β-conformable fractional operators in the Liouville–Caputo (LC) sense. For numerical solution, we present the two-step Adams–Bashforth numerical approach for the CF operator and the Adams–Moulton numerical method for fractional conformable operators in the LC sense. Lastly, numerical outcomes are demonstrated graphically for various choices of the fractional-order parameters.

Several deadly epidemics that have recognized as serious problems all over the world in the last few decades. Lassa hemorrhagic fever, coronavirus, dengue fever, malaria, and HIV are well-known deadly diseases in humans. In this research, we analysed the dynamics of the canine distemper virus (CDV) and rabies epidemics in the red fox population of the northern region of Italy with the help of time-fractional models. We performed our analysis in the new generalized Caputo non-classical derivative sense with the application of the Predictor–Corrector algorithm. We used the data of northern Italy for simulations and estimated the endemic equilibrium points for both CDV and rabies models. Also, we presented the local stability of disease-free equilibrium points. Some theorems are mentioned for the purpose of existence and uniqueness analysis. Our results are perfect for giving an idea of the dynamics of the CDV and rabies epidemic in northern Italy. The dynamics of the given solutions are specified with the help of necessary graphical simulations. The projected algorithm is so effective in finding the solutions of complex dynamical systems. By this study, we give an idea of how applied mathematics is directly connected to biological studies. The major scientific aim of this study is to understand the outbreaks of CDV and rabies on the population of the red foxes by using the texture of fractional mathematical models.

Mathematical modeling plays an important role to better understand the disease dynamics and designing strategies to manage quickly spreading infectious diseases in lack of an effective vaccine or specific antivirals. During this period, forecasting is of utmost priority for health care planning and to combat COVID-19 pandemic. In this study, we proposed and extended classical SEIR compartment model refined by contact tracing and hospitalization strategies to explain the COVID-19 outbreak. We calibrated our model with daily COVID-19 data for the five provinces of India namely, Kerala, Karnataka, Andhra Pradesh, Maharashtra, West Bengal and the overall India. To identify the most effective parameters we conduct a sensitivity analysis by using the partial rank correlation coefficients techniques. The value of those sensitive parameters were estimated from the observed data by least square method. We performed sensitivity analysis for R0to investigate the relative importance of the system parameters. Also, we computed the sensitivity indices for R0to determine the robustness of the model predictions to parameter values. Our study demonstrates that a critically important strategy can be achieved by reducing the disease transmission coefficient βsand clinical outbreak rate qato control the COVID-19 outbreaks. Performed short-term predictions for the daily and cumulative confirmed cases of COVID-19 outbreak for all the five provinces of India and the overall India exhibited the steady exponential growth of some states and other states showing decays of daily new cases. Long-term predictions for the Republic of India reveals that the COVID-19 cases will exhibit oscillatory dynamics. Our research thus leaves the option open that COVID-19 might become a seasonal disease. Our model simulation demonstrates that the COVID-19 cases across India at the end of September 2020 obey a power law.

In this paper, we will propose a novel system for remote detecting COVID-19 patients based on artificial intelligence technology and internet of things (IoT) in order to stop the virus spreading at an early stage. In this work, we will focus on connecting several sensors to work together as a system that can discover people infected with the Coronavirus remotely, this will reduce the spread of the disease. The proposed system consists of several devices called smart medical sensors such as: pulse, thermal monitoring, and blood sensors. The system is working sequentially starting by pulse sensor and end by blood sensor including an algorithm to manage the data given from sensors. The pulse sensor is devoted to acquire a high quality data using a smartphone equipped by a mobile dermatoscope with 20× magnification. The processing is used RGB color system to perform moving window to segment regions of interest (ROIs) as inputs of the heart rate estimation algorithm. The heart rate (HR) estimation is then given by computing the dominant frequency by identifying the most prominent peak of the discrete Fourier transform (DFT) technique. The thermal monitoring is used for fever detection using a smart camera that can provide an optimum solution for fever detection. The infrared sensor can quickly measure surface temperature without making any contact with a person’s skin. A blood sensor is used to measure percentages of white, red blood (WBCs, RBCs) volume and platelets non-invasively using the bioimpedance analysis and independent component analysis (ICA). The proposed sensor consists of two electrodes which can be used to send the current to the earlobe and measure the produced voltage. A mathematical model was modified to describe the impedance of earlobe in different frequencies (i.e., low, medium, and high). The COMSOL model is used to simulate blood electrical properties and frequencies to measure WBCs, RBCs and Platelets volume. These devices are collected to work automatically without user interaction for remote checking the coronavirus patients. The proposed system is experimented by six examples to prove its applicability and efficiency.