MODELING DENGUE TRANSMISSION WITH HUMAN AWARENESS AND STAGNANT WATER INDEX: ANALYSIS AND SIMULATION
By
Mamta Kumari DCT’S Dhempe College of Arts & Science, Panaji, Goa, India-403001
Email: mamtakumarii2014@gmail.com
Received: August 01, 2025; Revised: February 17, 2026; Accepted : February 20, 2026
DOI: https://doi.org/10.58250/jnanabha.2026.561P-4
Abstract
Dengue fever remains a major vector-borne health threat, particularly in regions where climatic conditions and human activities such as improper waste management and water storage support mosquito breeding. This paper improves the classical nonlinear SIR–SI host–vector framework by introducing an environmentally dependent mosquito recruitment function, λ(A) = λ0 + λ1A0, where A denotes a dimensionless Stagnant Water Index (SWI). This modification addresses a key limitation of earlier models, which assumed constant mosquito recruitment and therefore could not capture seasonal or ecological variability. By coupling the environmentally responsive recruitment term with human awareness (φ) and vector-control efforts (ψ), the proposed model captures dengue transmission dynamics more realistically under diverse environmental scenarios. We examine the existence and stability of both the disease-free equilibrium (DFE) and endemic equilibrium (EE), and compute the basic reproduction number R0 using the next-generation matrix approach. Numerical simulations establish that reducing stagnant-water accumulation (lower A), together with enhanced community awareness, considerably curbs peak infection and reduces R0. The results highlight the combined importance of ecological management and human behavioral responses in controlling dengue transmission.
2020 Mathematical Sciences Classification: 34D20; 92D30; 37N25; 92B05
Keywords and Phrases: Mathematical modeling; Dengue dynamics; Basic reproduction number; Stability analysis; Next-generation matrix; Mosquito-human interaction; Endemic equilibrium; Stagnant water index