A Dynamically Consistent Numerical Approach for the Ebola Virus Transmission Model with Fuzzy Parameters and Time Delay


== Abstract ==

The Ebola virus disease (EVD) is a major threat to human health, especially in Central West Africa. In this study, the transmission dynamics of EVD infection are studied using the Susceptible, Infected, Recovered, Deceased, and Pathogen (SIRDP) epidemic framework that prioritizes identifying and quantifying the sources of uncertainty in parameters. Conventional quantitative methods may believe that all measurements are exact, but in reality, data can often be imprecise or hard to measure. To overcome this challenge, fuzzy theory has been integrated into the model due to its flexibility in managing uncertainty. Additionally, this study considers the temporal dynamics of EVD transmission by integrating time delays, which makes the model fit the real-world simulation of disease progression. A sensitivity analysis of the reproductive number was also conducted to assess the impact of key parameters on the transmission dynamics. The behavior of the model has been numerically explored using various algorithms, such as the forward Euler method and the NonStandard Finite Difference (NSFD) scheme. Some significant numerical characteristics like positivity, convergence, and consistency have been assessed, which indicates that the NSFD method can capture the trends of EVD with fuzzy parameters. The proposed scheme maintains important characteristics of the traditional epidemic models and provides a stable approach for assessing EVD patterns in conditions of risks and unknown variables. The computational experiment confirms the theoretical conclusions and depicts the deficiencies of the normal finite difference approximations, notably for large step sizes, and supports the advantages of the NSFD approach in maintaining the structure of the model.OPEN ACCESS Received: 01/08/2024 Accepted: 16/10/2024

== Full document ==
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