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It is observed that the exposure to environmental factors such as indoors and outdoors air pollution, cigarette smoke, and allergens are highly related to asthma attacks. It is also reported that limited exposure to asthma riggers, cure due to medicine, the attacks of asthma can be minimized. In this paper, we formulate the dynamics of asthma with smoking and environmental factors classes in the fractional Caputo-Fabrizio (CF) framework to visualize its dynamical behaviour. We delineate the important properties of the CF derivative for the analysis of our model. The model is then analyzed for the basic properties and the uniqueness and existence of the hypothesized asthma system are investigated via the theory of fixed point. Furthermore, a novel numerical scheme is presented for the solution of our fractional system to illustrate the time series of asthma model. The dynamical behaviour of our asthma model is then highlighted numerically to show the impact of fractional-order ϧ on the system and to visualize the role of input factors on the dynamics of asthma disease. [ABSTRACT FROM AUTHOR]

In this study, we formulate a mathematical model in the framework of the Atangana-Baleanu fractional derivative in Caputo sense to study the transmission of tungiasis. In this formulation, interactions between the human host and the sand fleas are taken into consideration, including factors like infestation rate, incubation duration, and recovery rate. We calculate the basic reproduction parameter for the system, symbolized by R0 with the help of the next-generation matrix technique. A novel numerical scheme for encapsulating the non-local and memory-dependent aspects of the system is conceptualized via the Atangana-Baleanu fractional derivative. We prove the existence and uniqueness of the solution of the model of the infection and establish stability of the steady-states of the model. In addition to this, numerical simulations are carried out to evaluate the efficiency of interventions like campaigns for better sanitation and treatment, and to investigate the influence of various management techniques on the prevalence of tungiasis. The outcomes of the numerical simulations give us information about the possible efficacy of different control strategies in lowering the incidence of tungiasis. This research gives quantitative tools to enhance decision-making processes in public health treatments and advances our understanding of the dynamics of the tungiasis. [ABSTRACT FROM AUTHOR]

In this paper, we formulate the transmission phenomena of Hand–Foot–Mouth Disease (HFMD) through non-integer derivative. We interrogate the biological meaningful results of the recommended system of HFMD. The basic reproduction number is determined through next generation method and the impact of different parameters on the reproduction number is examined with the help of partial rank correlation coefficient (PRCC) technique. In addition, we concentrated on qualitative analysis and dynamical behavior of HFMD dynamics. Banach's and Schaefer's fixed-point theorems are used to analyze the uniqueness and existence of the solution of the proposed HFMD model. The HFMD system's Ulam–Hyers stability has been confirmed to be sufficient. To highlight the impact of the parameters on the dynamics of HFMD, we performed several simulations through numerical scheme to conceptualize the transmission route of the infection. To be more specific, numerical simulations are used to visualize the effect of input parameters on the systems dynamics. We have shown the key input parameters of the system for the control of infection in the society. [ABSTRACT FROM AUTHOR]

In this research work, we offer an epidemic model for monkeypox virus infection with the help of non-integer derivative as well as classical ones. The model takes into account every potential connection that can aid in the spread of infection among the people. We look into the model's endemic equilibrium, disease-free equilibrium, and reproduction number ℛ 0 . In addition to this, we concentrated on the qualitative analysis and dynamic behavior of the monkeypox virus. Through fixed point theorem, Banach's and Schaefer's are applied to study the existence and uniqueness of the solution of the suggested system of the monkeypox virus infection. We provide the necessary criteria for the recommended fractional system's Ulam–Hyers stability. Furthermore, a numerical approach is used to study the solution routes and emphasize how the parameters affect the dynamics of the monkey pox virus. The most crucial features of the dynamics of the monkeypox virus are noticed and suggested to decision-makers. [ABSTRACT FROM AUTHOR]

AbstractMeasles, a member of the Paramyxoviridae family and the Morbillivirus genus, is an infectious disease caused by the measles virus that is extremely contagious and can be prevented through vaccination. When a person with the measles coughs or sneezes, the virus is disseminated by respiratory droplets. Normally, the appearance of measles symptoms takes 10–14 d following viral exposure. Conjunctivitis, a high temperature, a cough, a runny nose, and a distinctive rash are some of the symptoms. Despite the measles vaccination being available, it is still widespread worldwide. To eradicate measles, the Reproduction Number (i.e. R0<1) must remain less than unity. This study examines a SEIVR compartmental model in the caputo sense using a double dose of vaccine to simulate the measles outbreak. The reproduction number R0 and model properties are both thoroughly examined. Both the local and global stabilities of the proposed model are determined for R0 less and greater than 1. To achieve the model’s global stability, the Lyapunov function is used while the existence and uniqueness of the proposed model are demonstrated In addition to the calculated and fitted biological parameters, the forward sensitivity indices for R0 are also obtained. Simulations of the proposed fractional order (FO) caputo model are performed in order to analyse their graphical representations and the significance of FO derivatives to illustrate how our theoretical findings have an impact. The graphical results show that the measles outbreak is reduced by increasing vaccine dosage rates. [ABSTRACT FROM AUTHOR]