Browsing by Author "January, Jeremiah"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Modeling and optimal control of rotavirus transmission dynamics with cost effectiveness
    (Elsevier B.V., 2025-12-29) January, Jeremiah; Mwanga, A. Gasper; Isack E.; Kibona b,; Shaban Mbare, Nyimvua
    An optimal control model for rotavirus transmission was formulated to minimize both the cost of implementing interventions and the burden of infection among children and care-givers. The model integrates five time-dependent control functions: vaccination of children (𝑢1), public health education (𝑢2), treatment of infected children (𝑢3), water treatment and sanitation (𝑢4), and hygiene promotion (𝑢5). Pontryagin’s Maximum Principle was applied to derive the necessary conditions for optimality, and numerical simulations were conducted using the Runge–Kutta method to determine the optimal time-dependent control profiles and corresponding epidemiological outcomes. Simulation results at 𝑡 = 220 days indicate a substantial reduction in rotavirus infections among children and caregivers when integrated controls are applied. The number of infected and hospitalized children (𝐼𝑏 and 𝐻𝑏) approach zero, while the vaccinated population (𝑉𝑏) reaches approximately 2.58 × 107, confirming the central role of vaccination in suppressing new infections. The concentration of environmental rotavirus particles (𝐶𝑟) also tends to zero, highlighting the combined efficacy of hygiene and sanitation interventions in reducing environmental transmission. Among the evaluated control strategies, the combination of vaccination, treatment, and hygiene (𝑆13) emerges as both the most cost-effective and epidemiologically impactful strategy. This approach achieves near-complete elimination of child infections at a moderate total cost of approximately $6.17×1011, yielding the best balance between health outcomes and economic feasibility. In contrast, the single-control strategies (𝑆1–𝑆5) achieve minimal infection reduction despite lower costs, while multi-control strategies involving all five interventions (𝑆17) provide marginal epidemiological improvement at substantially higher cost. The cost-effectiveness analysis, expressed as cost per health unit reduced, identifies vaccination (𝑢1) and treatment (𝑢3) as the primary contributors to financial cost, while hygiene adherence (𝑢5), sanitation (𝑢4), and education (𝑢2) offer strong epidemiological benefits with minimal marginal cost. This demonstrates that optimal disease control is achieved when vaccination and treatment are combined with sustained hygiene practices rather than through expensive full scale interventions. Overall, the results confirm that targeted multi control strategies particularly 𝑆13p rovide the most practical and sustainable pathway for reducing rotavirus transmission, minimizing infections, and optimizing public health expenditure.