A Mathematical and Optimal Control Model for Rabies Transmission Dynamics Among Humans and Dogs with Environmental Effects

TL;DR

This paper develops a mathematical model incorporating environmental factors and optimal control strategies to understand and reduce rabies transmission among humans and dogs, demonstrating the effectiveness of combined interventions.

Contribution

It introduces a novel deterministic model with environmental effects and applies optimal control theory to identify effective rabies intervention strategies.

Findings

Optimal control reduces rabies transmission effectively.

Vaccination and treatment are key to rabies elimination.

Higher contact rates among dogs increase transmission risk.

Abstract

This study presents a deterministic model to investigate rabies transmission dynamics, incorporating environmental effects and control strategies using optimal control theory. Qualitative and quantitative analyses reveal that the disease-free equilibrium is stable when the effective reproduction number $\mathcal{R}_e < 1$, and unstable when $\mathcal{R}_e > 1$. Mesh and contour plots illustrate an inverse relationship between $\mathcal{R}_e$ and control strategies, including dog vaccination, health promotion, and post-exposure treatment. Increased intervention reduces transmission, while higher contact rates among dogs raise $\mathcal{R}_e$. Numerical simulations with optimal control confirm the effectiveness of integrated strategies. Vaccination and treatment are identified as key interventions for achieving rabies elimination within five years.