Dynamical analysis and design of computational methods for nonlinear stochastic leprosy epidemic model

The application of fuzzy theory is vital in all scientific disciplines. The construction of mathematical models with fuzziness is little studied in the literature. With this in mind and for a better understanding of the disease, an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classical model of malaria transmission. The parameters β and δ, being function of the malaria virus load, are considered fuzzy numbers. Three steady states and the reproduction number of the model are analyzed in fuzzy senses. A numerical technique is developed in a fuzzy environment to solve the studied model, which retains essential properties such as positivity and dynamic consistency. Moreover, numerical simulations are carried out to illustrate the analytical results of the developed technique. Unlike most of the classical methods in the literature, the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.

Section: Non-standard Finite Difference (Nsfd) Schemementioning

confidence: 91%

Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment

Dayan¹,

Băleanu²,

Ahmed³

et al. 2023

“…Additionally, as desired, Fig. 3e displays the system's combined behavior (1)(2)(3)(4) without the delay effect. Figs.…”

Section: Computer Simulationsmentioning

confidence: 99%

“…According to a report, in 2003, Pakistan had 20,000 leprosy cases, and its ratio decreased from 2009 to 2018. The leprosy rate is highly associated with India, the African region is considered the second most highly affected, and Brazil is third [1]. In 2004, Meima et al investigated the effects of the current strategy to overcome leprosy, and the scenario presented that the following strategy will help reduce transmission.…”

Section: Introductionmentioning

confidence: 99%

Bio-Inspired Modelling of Disease Through Delayed Strategies

Nasir¹,

Băleanu²,

Raza³

et al. 2022

Self Cite

In 2020, the reported cases were 0.12 million in the six regions to the official report of the World Health Organization (WHO). For most children infected with leprosy, 0.008629 million cases were detected under fifteen. The total infected ratio of the children population is approximately 4.4 million. Due to the COVID-19 pandemic, the awareness programs implementation has been disturbed. Leprosy disease still has a threat and puts people in danger. Nonlinear delayed modeling is critical in various allied sciences, including computational biology, computational chemistry, computational physics, and computational economics, to name a few. The time delay effect in treating leprosy delayed epidemic model is investigated. The whole population is divided into four groups: those who are susceptible, those who have been exposed, those who have been infected, and those who have been vaccinated. The local and global stability of well-known conclusions like the Routh Hurwitz criterion and the Lyapunov function has been proven. The parameters' sensitivity is also examined. The analytical analysis is supported by computer results that are presented in a variety of ways. The proposed approach in this paper preserves equilibrium points and their stabilities, the existence and uniqueness of solutions, and the computational ease of implementation.

“…The non-convergence behavior of Euler's approach at a slightly higher value remains the same. One of the most exciting features of the above graphs is the consistency of the NSFD method across all step sizes, as many other classical methods such as Euler Maruyama, Euler's Stochastic, and RK-4 do not preserve it at large step sizes, as discussed in [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Standard finite difference schemes and stochastic techniques violate dynamical properties and produce negative and unbounded solutions that have no physical meaning, as discussed by Arif et al Finite difference techniques with fuzziness exhibit similar behavior.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Modeling of Computer Virus Propagation with Fuzzy Parameters

Alhebshi¹,

Ahmed²,

Băleanu³

et al. 2023

Typically, a computer has infectivity as soon as it is infected. It is a reality that no antivirus programming can identify and eliminate all kinds of viruses, suggesting that infections would persevere on the Internet. To understand the dynamics of the virus propagation in a better way, a computer virus spread model with fuzzy parameters is presented in this work. It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity, which depends on the quantity of virus. Considering this, the parameters β and γ being functions of the computer virus load, are considered fuzzy numbers. Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models. The essential features of the model, like reproduction number and equilibrium analysis, are discussed in fuzzy senses. Moreover, with fuzziness, two numerical methods, the forward Euler technique, and a nonstandard finite difference (NSFD) scheme, respectively, are developed and analyzed. In the evidence of the numerical simulations, the proposed NSFD method preserves the main features of the dynamic system. It can be considered a reliable tool to predict such types of solutions.