e-ISSN: 2582-5208 International Research Journal of Modernization in Engineering Technology and Science ( Peer-Reviewed, Open Access, Fully Refereed International Journal ) Volume:06/Issue:05/May-2024 Impact Factor- 7.868 www.irjmets.com www.irjmets.com @International Research Journal of Modernization in Engineering, Technology and Science [11038] OPTIMIZING VACCINATION STRATEGIES TO REDUCE CONJUNCTIVITIS TRANSMISSION: MATHEMATICAL MODELING INSIGHTS FROM KENYA Charles Ndambuki Muli *1 , Ancent Makau Kimulu *2 *1 Department Of Mathematics And Statistics, Machakos University, P.O. Box 136-90100, Machakos , Kenya. *2 Department Of Mathematics And Actuarial Science, Kenyatta University, P.O. Box 43844-00100, Nairobi, Kenya. DOI : https://www.doi.org/10.56726/IRJMETS57623 ABSTRACT Conjunctivitis is a widespread condition with significant public health implications, but its potential impact on transmission patterns due to vaccination programs, particularly in Kenya, remains underexplored. The main aims of this study to investigate the role of vaccination in preventing conjunctivitis spread and related complications. A deterministic mathematical model was developed in an attempt to simulate conjunctivitis incidence, considering factors like population size, contact rates, and vaccination efficacy. The basic reproduction number (R₀) was calculated using the next-generation matrix method. Stability analysis of the disease-free equilibrium (DFE) showed stability will occur when R₀ < 1 and instability when R₀ > 1. Numerical computations using the MATLAB ode45 solver indicated that increased vaccination campaigns reduce the infected population. This implies that vaccination strengthens the immune response against the infection, lowering the risk of severe outcomes like vision loss. This study is vital for understanding the potential impact of effective vaccination programs on conjunctivitis transmission in Kenya, aiding policy-makers and public health practitioners in developing effective disease control measures. Keywords: Conjunctivitis, Mathematical Modeling, Next Generation Matrix, Transmission Dynamics, Vaccination Campaigns. I. INTRODUCTION Pink eye, also known as conjunctivitis, is an inflammation of the conjunctiva. The conjunctiva is a thin, transparent tissue that covers the inner surface of the eyelid and the white section of the eye. It is a highly infectious disease that causes redness, irritation, abundant weeping, and a yellow discharge. Bacterial and viral infections are common causes of pink eye, but it can also be caused by allergies and irritants, as noted by [1]. Several bacteria may lead to bacterial conjunctivitis: Streptococcus pneumoniae, Haemophilus influenzae, and Staphylococcus aureus. But this type of conjunctivitis often does not have a latent phase in an infectious way and usually shows symptoms quite fast after being around those bacteria, like yellow or green stuff coming out, eyelids getting crusty, and feeling uncomfortable [2,3]. For that purpose, to effectively prevent and control bacterial conjunctivitis, it is crucial to understand how it spreads. Vaccine activities have played an essential part in reducing the global load of infectious diseases [4]. By considering conjunctivitis spreading in Kenya, beginning a vaccine campaign has the potential to significantly decrease the disease's spread. Mathematical models are a powerful tool to check the potential impacts of these vaccine efforts on disease spreading patterns. Mathematical models, which involve features such as how many people get vaccinated, how well the vaccines work, and population demos, can give useful thoughts about how vaccination might affect conjunctivitis spreading in Kenya. Numerous research areas have used math modeling to better grasp how bacterial conjunctivitis gets passed on and to evaluate ways to stop it. For example, [5] checked if closing schools could prevent bacterial conjunctivitis from spreading among kids. [1] studied how rotavirus vaccines affect epidemiology to stop bacterial conjunctivitis outbreaks in healthcare areas. Moreover, [6] looked at how environmental factors affect the spreading of bacterial conjunctivitis, while [4] tried to find the best ways to vaccinate people to stop infections from happening again.