Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya

Micro, Small and Medium Enterprises (MSMEs) play a significant role in employment, income generation and Gross Domestic Product (GDP) in Kenya, but many enterprises remain financially weak, carry heavy loan debt and struggle to repay. This study formulates a nonlinear ordinary differential equation (ODE) model to investigate the interaction between financial literacy, financial health, loan burden, cash reserves and stressors in the business environment for MSMEs in Kenya. The model provides a flexible tool for analysing the equilibrium behavior, positivity, boundedness, local stability and parameter sensitivity. The analysis shows that under economically sensible assumptions the model solutions are non-negative and bounded. An asymptotic stable equilibrium is constructed and calculated to be cash exhausted with the baseline parameter set and found to be locally stable. Sensitivity results show that financial efficacy and literacy intervention have positive effects on financial health, while literacy decay, debt-servicing and business stressors have negative effects on enterprise sustainability. The phase portrait and sensitivity visualization illustrate the financial-health--loan-burden trajectory and the relative influence of the principal model parameters. The study yields a mathematical framework for designing financial literacy programs, credit-management strategies, and interventions to support loan repayment that can help improve the resilience of MSMEs and their ability to repay loans.