| dc.description.abstract | Tuberculosis (TB) remains a major global health concern, particularly in overcrowded healthcare and institutional settings where transmission risk is elevated. Mathematical modeling provides insight into disease dynamics and treatment effects in such environments. The study focused on modeling TB spread and treatment variations in care institutions. Care institutions are facilities that offer essential health, social and rehabilitative services to individuals needing ongoing support due to age, illness, or disability. They include hospitals, rehabilitation centers, nursing homes, prisons and shelters where exposure duration and overcrowding are critical factors, and aim to provide treatment, preventive care and daily assistance in a safe environment (Ministry of Health Kenya, 2025). Prior work by Beggs et al. (2003) emphasized TB transmission in confined spaces but lacked detail on treatment variation and duration of exposure common in care settings. The present study develops a compartmental model using ordinary differential equations, simulated in MATLAB and Mathematica. The basic reproduction number (R0) was derived analytically, incorporating variables like infectivity rates, progression probabilities, and relapse dynamics. Using parameter estimates relevant to Kenyan institutions, the calculated R0 was 0.00022, indicating that TB would eventually be eradicated under current conditions. Variation of the parameter values within the range of the parameters had impact on the model and indicated that the model was sensitive and it was graphically illustrated. Sensitivity analysis showed that parameter variations significantly influenced transmission outcomes, enhancing confidence in the model’s predictive accuracy. Robustness of the SV EIeInTnTfR model were achieved
using the basic reproduction number. The value obtained from the basic reproduction number after inserting the parameter values given in table 3 in the formula for the basic reproduction number was below unit and indicated that TB disease died out hence the model was stable. Simulations revealed that full treatment regimens significantly reduced TB prevalence compared to partial treatment scenarios. These results suggest
that improving treatment adherence and completing full therapy cycles in care institutions can drastically reduce TB transmission. Stakeholders and policymakers should consider these findings to enhance control strategies, optimize resource allocation, and support evidence-based policy interventions within institutional settings. | en_US |
