Discrete Dynamics in Nature and Society

In this paper, a fractional model in the Caputo sense is used to characterize the dynamics of HPV with cervical cancer. Generalized mean value theorem has been used to examine whether the infection model has a unique positive solution. The model has two equilibrium points: the disease-free point and the endemic point. The examination of the system’s local and global stability is provided in terms of the basic reproductive number . The global stability analysis has been carried out using an appropriate Lyapunov function and the LaSalle invariant principle. The results demonstrate that in the infection model, if , then the solution converges to the disease-free equilibrium, which is both locally and globally asymptotically stable. Whilst , the endemic equilibrium is considered to exist. Simulations are implemented via a finite difference method with Grünwald-Letnikov discretization approach for Caputo derivative operator to define how changes in parameters impact the dynamic behavior of the system using Matlab.

The development of the textile and apparel (T&A) industry has led to an increasing focus on recycling used products. Remanufactured product quality raises consumer concerns, and blockchain can effectively solve this problem. We establish a closed-loop supply chain (CLSC) in which a manufacturer, a retailer, or a third-party recycler collects used T&A products to examine the most efficient recycling mode with and without blockchain and the impact of blockchain on CLSC decisions. The results show that (1) if the manufacturer’s recycling cost coefficient is relatively low, used T&A products are collected directly by the manufacturer. Otherwise, the responsibility for recycling used T&A products falls to the retailer or the third-party recycler. It is noteworthy that the manufacturer’s choice of recycling mode remains unchanged whether a blockchain is implemented or not. (2) The implementation of blockchain by the manufacturer and the retailer can increase profits and consumers also benefit when the cost of validating blockchain units remains below a certain threshold. (3) When the recycling cost coefficient exceeds a certain threshold, the implementation of blockchain increases prices and recycling rates. These findings offer CLSC members’ management insights into how to select the optimal recycling mode and the consequences of implementing blockchain.

This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model.

The dengue virus is the most dangerous one that mosquitoes may spread to people. Despite attempts by the government, dengue outbreaks are becoming increasingly common in Bangladesh. Interventions in public health rely heavily on KAP (knowledge, attitude, and practice) studies. The primary goal of this research is to forecast the occurrence of dengue disease in the city of Dhaka using methods from machine learning and time series analysis and then to compare the models in order to find the one with the lowest MAPE. From January 2016 through July 2021, monthly data were retrieved for this study from WHO and the Directorate General of Health and Services (DGHS). According to the findings of this research, neural networks outperform time series analysis when it comes to making predictions. The best-fitted neural network (NN) model was found in model 04 with 05 hidden layers which produced the minimum error model with the value of error 0.003032557, and the values of RMSE and MAPE are 7.588889e − 06 and 1.15273, respectively, for the prediction of the dengue fever in Dhaka city. In contrast, the original dengue data in the time series analysis is not stationary. Take the difference and run the unit root test by the augmented Dickey–Fuller (ADF) test to make it stationary. The dengue data series is stationary at the first-order difference, as evidenced by the ACF and PACF, which show no noticeable spike in the first-order difference. The ARIMA (6, 1, 1) model with the lowest AIC = −251.8, RMSE = 0.0310797, and MAPE = 15.2892 is the best choice model for predicting the dengue death rate. Therefore, from these two models, the NN model gives better prediction performance with the lowest value of MAPE. So, the neural network gives better prediction performance than time series analysis. The NN model forecasted 12-month death rates of dengue fever that suggest the death rate in dengue fever falling month by month. This study is more innovative than any other research because this research approach is different from any other research approach. The model selection criteria are based on the most effective performance metrics MAPE, indicating the lowest error and better prediction performance. Therefore, from this research, the author suggests machine learning gives better prediction performance than time series analysis for any other prediction performance.

In this paper, the limit cycles and local bifurcation of critical periods for a class of switching equivariant quartic system with two symmetric singularities are investigated. First, through the computation of Lyapunov constants, the conditions of the two singularities to become the centers are determined. Then, we prove that there are at most 18 limit cycles with a distribution pattern of 9-9 around the two symmetric singular points of the system. Numerical simulation is conducted to validate the obtained results. Furthermore, by calculating the period constants, we determine the conditions for the critical point to be a weak center of finite order. Finally, the number of local critical periods that bifurcate from the equilibrium point under the center conditions is discussed. This study presents the first example of a quartic switching smooth system with 18 limit cycles and 4 local critical periods bifurcating from two symmetric singular points.

Banks are financial institutions that are crucial to the accomplishment of development objectives because they transfer money from surplus to deficit parties. This study examines the competition, survival, and performance constraints of commercial banks in Ethiopia using the DEA and CAMEL frameworks from 2015 to 2020. The nonparametric (DEA) approach was applied to approximate the overall technical efficiency score of the banks under consideration. The empirical study used twelve private commercial banks operating in Ethiopia, excluding four banks because of a lack of appropriate and audited financial data and no risk assessment between the study periods. The result of the study reveals that under CRS, except for Abyssinia, Anbesa, and Nib International Banks, the remaining banks are more efficient. Under VRS, while Abyssinia Bank was less efficient, other banks were found to be more efficient. Under scale efficiency, Abyssinia, Anbesa, and Nib International Banks were found to be less efficient, while the remaining banks were more efficient. The composite ranking of the CAMEL framework portrays that Awash International Bank, Zemen, and Wegagen Banks were found in the top three ranks, while Cooperative Bank of Oromia, Dashen, and Abyssinia Banks were found in the bottom position. The regression result demonstrates that the ratios of total capital to total assets, loans to assets, total loans to total deposits, and CAR have a positive effect on bank profitability, whereas the ratio of total loans to the number of branches has a statistically negative and significant influence on the return on assets.