Abstract
This article presents the dynamical analysis of the stochastic leprosy epidemic model. Positivity and boundedness are the criteria used in the deterministic model. A primary technique is known as the Euler Maruyama used in the solution of the said model. The standard computational methods will evaluate the design stability and efficiency based on the chosen criteria. The traditional computational methods like the stochastic Euler and the stochastic Runge Kutta fail to restore the essential features of biological problems. However, our proposed approach, the stochastic non-standard finite difference (NSFD), is used and found to be efficient, cost-effective, and accommodates all the desired feasible properties. Our method achieves all-time convergence against the backdrop of other classical techniques that perform conditionally or fail over a long period. In the end, a comparison between this scheme and the existing ones reviews the novelty of our approach.
Highlights
In 2018, Giraldo et al studied a mathematical model based on nonlinear ordinary differential equations
We studied the dynamics of a leprosy disease in humans using a mathematical model in which the human population is divided into four subpopulations, respectively
The physical interpretation of the model is presented as follows: f represents a fraction of humans who developed multibacillary leprosy, 1-f portrays a fraction of humans who developed paucibacillary leprosy, ρ describes the natural growth rate of humans, βp delineates the contact rate of paucibacillary leprosy individuals, βm shows the contact rate of multibacillary leprosy individuals, θ presents the rate at which asymptomatic individuals may be symptomatic individuals, μm depicts the death rate of the infected individuals by multibacillary leprosy, while μ is the natural death rate of individuals
Summary
In 2018, Giraldo et al studied a mathematical model based on nonlinear ordinary differential equations. In 2018, Varella et al presented the mathematical model related to leprosy type infection: a case study of the spread of leprosy in Brazil [2]. In 2021, Marathi et al developed a multi-dimensional mathematical model for the transmission of leprosy disease [3]. In 2013, Ghayas et al studied leprosy disease transmission dynamics: a case of Gilgit-Baltistan, Pakistan [7]. In 2013, Chiyaka et al developed numerical and theoretical analysis for transmission dynamics of leprosy disease [9]. Arco et al, in 2016, diagnosed the leprosy symptoms and transmission modes [10], while Le et al, in 2018, investigated the control plans for the disease-like infections: a case study of monitoring and detection in China [11].
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