Browsing by Author "January, Jeremiah"

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Examination Seating Optimization Using Graph Coloring and Combinatorial Design
(ELSEVIER, 2026) Kibona, Isack E.; January, Jeremiah; Matimbwa, Hadija; Nchia, Edwin; Matungwa, William; Vuai, Said A.H.
This paper presents an optimization approach for exam seating in universities with limited infrastructure, based on a mixed-course allocation model. Students in different courses share rooms while maintaining spatial separation to improve academic integrity. The model incorporates a theoretical probability of interaction, which decreases as the number of mixed courses in a room increases. Using real data with 5175 students, the proposed model significantly improves upon the traditional method. Although the traditional approach required 35 rooms with a total capacity of 7269, the proposed model utilized only 12 large rooms, leaving 23 rooms unused and saving about 2475 seats. The unused space within the occupied rooms was minimal (approximately 29 seats), indicating near-optimal utilization. The invigilation requirement was reduced from at least 70 to 36, achieving nearly 50% savings. Small- enrollment and carryover courses are efficiently integrated and sorted. The model is formulated using graph coloring and combinatorial optimization, supported by a simple allocation algorithm
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.