This paper presents an analysis and numerical simulation of financial crime population dynamics using fractional order calculus and Newton's polynomial. The dynamics of financial crimes are modeled as a fractional-order system, which is then solved using numerical methods based on Newton's polynomial. The results of the simulation provide insights into the behavior of financial crime populations over time, including the stability and convergence of the systems. The study provides a new approach to understanding financial crime populations and has potential applications in developing effective strategies for combating financial crimes. Fractional derivatives are commonly applied in many interdisciplinary fields of science because of its effectiveness in understanding and analyzing complicated phenomena. In this work, a mathematical model for the population dynamics of financial crime with fractional derivatives is reformulated and analyzed. A fractional-order financial crime model using the new Atangana-Baleanu-Caputo (ABC) derivative is introduced. The reproduction number for financial crime is calculated. In addition, the relative significance of model parameters is also determined by sensitivity analysis. The existence and uniqueness of the solution in consideration of the ABC derivative are discussed. A number of conditions are established for the existence and Ulam-Hyers stability of financial crime equilibria. A numerical scheme is presented for the proposed model, starting with the Caputo-Fabrizio fractional derivative, followed by the Caputo and Atangana-Baleanu fractional derivatives. Finally, we solve the models with fractal-fractional derivatives.

This paper aims to extend the spore dispersal model to the Healthy-Latent-Infectious-Removed (HLIR) epidemic model for assessing the severity of rice blast disease. The model was solved by the Finite Difference Method (FDM). The results of the model were compared to data from the Prachinburi Rice Research Center (PRRC) on the severity of rice blast disease. Because of a small error, the comparison results showed good agreement between the PRRC data and the simulation by looking at the value of Willmott's index of agreement ( $d$). The first bed $d$ was 0.7166, while the second bed $d$ was 0.6421, indicating the model's performance. Furthermore, the optimal parameter, the fraction of spores deposited on the crop, was determined to be 0.173 and 0.016 for beds 1 and 2, respectively. The model can simulate and analyze rice blast outbreaks for educational purposes in future preparedness planning.

Cassava mosaic disease (CMD) is caused by a virus transmitted by the whitefly. This disease can destroy cassava at any stage of its growth and it resulted in lower cassava yields. In this paper, we developed a mathematical model for the epidemic of cassava mosaic disease with a deterministic model which has saturation incidence rates. This model aims to explain the effect of vectors on cassava disease outbreaks. First, this model was analyzed using standard dynamic methods to determine the behavior of the solution. We found the existence and condition of disease-free and endemic steady state. The basic reproductive number ( $R_0$) is obtained by using the next-generation method which $R_0$ helps assess the ability to spread infectious diseases. Second, the stability of the steady state was analyzed, then we obtain the condition of existence of local stability and global stability at each steady state of this model. Third, analysis of the sensitivity indices in the threshold number to determine the effect of the various parameters. Finally, the results of the theoretical model were validated by numerical simulations. It is represented by various graphs converging at a steady state and stable.

We investigated the leptospirosis epidemic model by using Caputo and Fabrizio fractional derivatives. Picard's successive iterative method and Sumudu transform are taken into consideration for developing the iterative solutions for the leptospirosis disease. Employing nonlinear functional analysis, the stability and uniqueness of the proposed model are established. Sensitivity analysis is taken into account to highlight the most sensitive parameters corresponding to the basic reproductive number. Various solutions to the proposed system have been interpolated by graphs with the application of Matlab software.

Leaf brown spot, caused by fungi, is a terrible plant disease, and it can significantly reduce the quality and quantity of rice. In this paper, we developed the model based on leaf brown spot disease development and considered a preventive treatment using botanical fungicide. In addition, we develop a model with suitable optimal control strategies. The result shows disease-free equilibrium is asymptotically stable when $R_0>1$. In contrast, the endemic equilibrium is asymptotically stable when $R_0>1$. The obtained optimal control to can reduce the number of infected plants compared to that without control. In addition, the analytical results were confirmed by numerical simulations of the occurrence of the theoretical results.

In this research, we reformulate and analyze a co-infection model consisting of Chagas and HIV epidemics. The basic reproduction number $R_0$ of the proposed model is established along with the feasible region and disease-free equilibrium point $E^0$. We prove that $E^0$ is locally asymptotically stable when $R_0$ is less than one. Then, the model is fractionalized by using some important fractional derivatives in the Caputo sense. The analysis of the existence and uniqueness of the solution along with Ulam-Hyers stability is established. Finally, we solve the proposed epidemic model by using a novel numerical scheme, which is generated by Newton polynomials. The given model is numerically solved by considering some other fractional derivatives like Caputo, Caputo-Fabrizio and fractal-fractional with power law, exponential decay and Mittag-Leffler kernels.

In this study, the COVID-19 epidemic model is established by incorporating quarantine and isolation compartments with Mittag-Leffler kernel. The existence and uniqueness of the solutions for the proposed fractional model are obtained. The basic reproduction number, equilibrium points, and stability analysis of the COVID-19 model are derived. Sensitivity analysis is carried out to elaborate the influential parameters upon basic reproduction number. It is obtained that the disease transmission parameter is the most dominant parameter upon basic reproduction number. A convergent iterative scheme is taken into account to simulate the dynamical behavior of the system. We estimate the values of variables with the help of the least square curve fitting tool for the COVID-19 cases in Pakistan from 04 March to May 10, 2020, by using MATLAB.