Sensitivity analysis and numerical simulation of the dynamics of cholera transmission with vaccination and pathogen mutation: Implications towards control in Kenya

Abstract

This study applies sensitivity and a numerical simulation of a deterministic cholera transmission model to consider vaccination, pathogen changes, sanitation and environmental contamination. The basic reproduction number ($R_0$) was calculated through next-generation matrix method and a base value of $R_0 = 0.78398$ was found. All model parameters were also normalized to identify which ones have the highest effect on the transmission of cholera. A vaccine efficacy of mutant strains of -1.2188, mutant strain recovery rate of -0.8403, and vaccination rate of -0.2578 are the most influential parameters to reduce $R_0$. Mutant shedding rate ($\eta_2 = +0.2237$), recruitment rate ($\Lambda = +0.2681$) and mutant strain transmission rate ($\beta_2 = +0.6996$), however, are the strongest drivers of disease spread. Numerical simulations with MATLAB's solver ode45 show that the infection prevalence and environmental bacterial concentration decrease by incorporating increased vaccination coverage and higher vaccine efficacy, hygiene compliance, and sanitation effort. Together with higher transmission rates, higher rate of bacterial shed and mutation rates increase disease persistence. Overall, the study finds an integrated approach to cholera control through a combination of vaccination, treatment, hygiene promotion, environmental sanitation, and pathogen surveillance to be crucial for achieving sustainable results in Kenya. Policy recommendations are given to optimize resource allocation in several different intervention pathways.