Optimal Control of Typhoid Fever Transmission With Imperfect Diagnosis and Multiple Interventions

Résumé

Typhoid fever persists in regions with poor sanitation and weak healthcare infrastructure, exacerbated by diagnostic inaccuracies—specifically false-negative test results—that leave infectious individuals untreated and sustain transmission. This study extends a deterministic compartmental model (PSIDT) to incorporate the epidemiological impact of imperfect diagnosis. Applying Pontryagin’s maximum principle, optimal control schedules are derived for four interventions: vaccination, diagnostic improvement, enhanced treatment, and water, sanitation, and hygiene (WASH) programs. Numerical simulations demonstrate that integrating these interventions reduces both infectious and misdiagnosed cases by more than 95% within 50 days. Incremental cost-effectiveness ratio (ICER) analysis reveals that improving diagnostic accuracy alone is the most cost-effective single strategy, costing 4.35 thousand Naira per averted infection, while the combined strategy averts the highest number of infections (950 per 1,000 cases) while maintaining a favorable ICER. Consequently, enhancing diagnostic accuracy should be prioritized alongside comprehensive public health measures in typhoid-endemic regions, as this optimal control framework offers practical, data-driven guidance for resource allocation.