A mathematical model for typhoid-helminth co-infection with typhoid-only treatment and persistent symptoms

Typhoid fever and helminthiasis are co-endemic in many low-resource settings and frequently present with overlapping clinical symptoms, complicating diagnosis and treatment. In practice, patients are often treated for typhoid fever alone, which may lead to temporary symptom relief while underlying helminth infection remains unrecognized. To investigate the epidemiological consequences of this scenario, we developed and analyzed a deterministic compartmental model that incorporates typhoid-helminth co-infection, a shared environmental transmission pathway, and a typhoid-only treatment strategy. The model possesses a disease-free steady state and a threshold reproduction metric that determines whether infection dies out or persists. Analytical results establish conditions for stability of both disease-free and endemic equilibria, while sensitivity analysis identifies the most influential parameters governing transmission. Simulation results indicate that enhanced typhoid treatment lowers typhoid prevalence but does not eliminate the total symptomatic burden when helminth infection is untreated. In contrast, improvements in environmental sanitation substantially reduce both infections and co-infection by limiting shared transmission pathways. These findings provide a mathematical explanation for persistent symptoms following typhoid treatment in co-endemic regions and highlight the importance of integrated diagnostic, therapeutic, and environmental interventions. The study underscores that sustainable reduction of disease burden requires coordinated strategies that address co-infection and environmental transmission rather than single-disease control alone.