Comparative analysis of time series prediction models for visceral leishmaniasis:based on SARIMA and LSTM

Visceral leishmaniasis, a severe health disorder, is attributed to the microscopic parasite Leishmania. The parasitic illness possesses the capacity to pose a significant risk to human life and exhibits a variable prevalence across people worldwide. Using time series prediction techniques for VL might offer valuable insights to aid public health professionals in strategizing and implementing effective measures for VL prevention. This study presents a comparative analysis of time series forecasting techniques, specifically focusing on two methods: SARIMA and LSTM recurrent neural networks. Forecast performance evaluation involves utilizing monthly VL data acquired from district health offices from January 2000 to December 2021. An assessment of the model’s performance is conducted to ascertain its efficacy. According to the evaluation conducted using three metrics, namely mean average precision (MAP), root mean square (RMS), and mean absolute error (MA), the findings indicate that the LSTM model outperforms the SARIMA model in terms of forecasting monthly conditions. The discovery implies that the LSTM approach may be better suited for predicting VL incidents and has the potential to contribute to the formulation of efficient preventive measures. Furthermore, it is suggested that future studies should investigate the possibility of integrating SARIMA and LSTM techniques to improve VL forecasts’ precision

Modeling and Analysis of a Fractional Visceral Leishmaniosis with Caputo and Caputo–Fabrizio derivatives

Visceral leishmaniosis is one recent example of a global illness that demands our best efforts at understanding. Thus, mathematical modeling may be utilized to learn more about and make better epidemic forecasts. By taking into account the Caputo and Caputo-Fabrizio derivatives, a frictional model of visceral leishmaniosis was mathematically examined based on real data from Gedaref State, Sudan. The stability analysis for Caputo and Caputo-Fabrizio derivatives is analyzed. The suggested ordinary and fractional differential mathematical models are then simulated numerically. Using the Adams-Bashforth method, numerical simulations are conducted. The results demonstrate that the Caputo-Fabrizio derivative yields more precise solutions for fractional differential equations

Analysis, modeling and simulation of a fractional-order influenza model

The primary goal of this study is to provide a novel mathematical model for Influenza using the Atangana–Baleanu Caputo fractional-order derivative operator (ABC-Operator) in place of the standard operator. There will be an examination of how the influenza-positive solutions reacts to real-world data. The fractional Euler Method will be utilized to reveal the dynamics of the influenza mathematical model. Both the stability of the disease-free equilibrium and the endemic equilibrium points, two symmetrical extrema of the proposed dynamical model, are examined. It will be shown, using numerical comparisons, that the findings obtained by employing the fractional-order model are considerably more similar to certain actual data than the integer-order model's results. These should shed light on the significance of fractional calculus when confronting epidemic risks

Improving Influenza Epidemiological Models under Caputo Fractional-Order Calculus

The Caputo fractional-order differential operator is used in epidemiological models, but its accuracy benefits are typically ignored. We validated the suggested fractional epidemiological seasonal influenza model of the SVEIHR type to demonstrate the Caputo operator’s relevance. We analysed the model using fractional calculus, revealing its basic properties and enhancing our understanding of disease progression. Furthermore, the positivity, bounds, and symmetry of the numerical scheme were examined. Adjusting the Caputo fractional-order parameter α = 0.99 provided the best fit for epidemiological data on infection rates. We compared the suggested model with the Caputo fractional-order system and the integer-order equivalent model. The fractional-order model had lower absolute mean errors, suggesting that it could better represent sickness transmission and development. The results underline the relevance of using the Caputo fractional-order operator to improve epidemiological models’ precision and forecasting. Integrating fractional calculus within the framework of symmetry helps us build more reliable models that improve public health interventions and policies

Mathematical modeling and stability analysis of the novel fractional model in the Caputo derivative operator: A case study

The fundamental goal of this research is to suggest a novel mathematical operator for modeling visceral leishmaniasis, specifically the Caputo fractional-order derivative. By utilizing the Fractional Euler Method, we were able to simulate the dynamics of the fractional visceral leishmaniasis model, evaluate the stability of the equilibrium point, and devise a treatment strategy for the disease. The endemic and disease-free equilibrium points are studied as symmetrical components of the proposed dynamical model, together with their stabilities. It was shown that the fractional calculus model was more accurate in representing the situation under investigation than the classical framework at α = 0.99 and α = 0.98. We provide justification for the usage of fractional models in mathematical modeling by comparing results to real-world data and finding that the new fractional formalism more accurately mimics reality than did the classical framework. Additional research in the future into the fractional model and the impact of vaccinations and medications is necessary to discover the most effective methods of disease control