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Journal of Applied Nonlinear Dynamics 14(3) (2025) 745--755 | DOI:10.5890/JAND.2025.09.015

Santosh Kumar Sharma$^1$, Sourav Rana$^2$, Amar Nath Chatterjee$^1$

$^1$ Department of Mathematics, K.L.S. College, Magadh University, Bodh Gaya, India

$^2$ Department of Statistics, Visva-Bharati University, Santiniketan, India

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Abstract

Dengue infection primarily occurs in tropical and subtropical regions. Climate change exacerbates the transmission of dengue fever. Therefore, stochastic modeling is significantly more efficient than a deterministic model. In this context, we work with deterministic and stochastic differential equation models. We have calculated the basic reproduction number ($R_0$) at the point when the disease-free equilibrium state is stable. The progression of the infection is contingent upon the value of $R_0$, and the disease can be effectively managed when $R_0$ is less than 1. Furthermore, the presence of the disease becomes apparent when the basic reproduction number ($R_0$) exceeds 1. This study enhances our comprehension of the transfer of infection between human hosts and mosquito vectors. In order to analyze the stochastic model, we employ the Euler-Maruyama and stochastic Runge-Kutta techniques. Additionally, we present the stochastic nonstandard finite difference scheme (SNSFD), which maintains the model's fundamental features, such as positivity, boundedness, and dynamic consistency, regardless of the chosen step size. The numerical results obtained from our stochastic model provide support for the validity of the stochastic differential equation model and its analytical findings.

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