A Mathematical Model for Typhoid Fever Transmission Incorporating Environmental Pathogen Dynamics and Treatment Interventions

Abstract

Typhoid fever remains a significant public health burden in developing countries and is primarily transmitted through contaminated food and water. This study develops a deterministic compartmental model incorporating environmental pathogen dynamics to better understand typhoid transmission and evaluate treatment interventions. The model extends the classical SEIR framework by introducing a pathogen concentration compartment (P), which captures indirect transmission through environmental contamination. The Disease-Free Equilibrium (DFE) and Endemic Equilibrium points are derived, and the basic reproduction number (R₀) is computed using the Next Generation Matrix method for both treatment and non-treatment scenarios. The stability of the Disease-Free Equilibrium is analyzed using the Routh-Hurwitz criterion. The results demonstrate that treatment significantly reduces the basic reproduction number compared with the non-treatment scenario. This finding confirms that treatment interventions can reduce secondary infections and disease burden, emphasizing the importance of combining effective treatment strategies with environmental hygiene measures to achieve optimal typhoid disease control.