Mathematical Formulation and Analytical Investigation of a SEIVTR Model for Zika Virus Transmission Dynamics with Dual Transmission Pathways
Keywords:
Zika Virus, SEIVTR Model, Basic Reproduction Number, Next-Generation Matrix, Disease-Free EquilibriumAbstract
Zika virus (ZIKV), a flavivirus primarily transmitted by Aedes aegypti mosquitoes and increasingly through sexual contact, constitutes a persistent global public health threat due to its association with microcephaly and neurological complications. Despite a growing body of epidemiological modeling literature, most existing frameworks either treat vector-borne and sexual transmission in isolation or neglect clinical case management pathways. This study presents the formulation and rigorous mathematical analysis of a novel six-compartment SEIVTR (Susceptible-Exposed-Infected-Victim-Treatment-Recovered) deterministic model that integrates both mosquito-borne and sexual transmission dynamics within a unified framework. The model is characterized by a system of six nonlinear ordinary differential equations governing a closed human–Aedes aegypti population. Key analytical results include: proof of solution positivity and uniform boundedness within a biologically invariant region; derivation of the disease-free equilibrium Z₀ and endemic equilibrium E₀; computation of the basic reproduction number R₀ ≈ 2.37 (with vector-borne component R₀(v) = 1.95 and sexual component R₀(s) = 0.42) via the Next-Generation Matrix method; and local asymptotic stability analysis demonstrating that Z₀ is stable when R₀ < 1 and E₀ is stable when R₀ > 1. The model's R₀ aligns closely with empirical estimates from major outbreak settings including Brazil and French Polynesia, supporting its validity. The analytical framework established herein provides a theoretically rigorous, mathematically validated foundation for designing and evaluating targeted Zika control strategies.
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