Modeling and optimal control analysis of transmission dynamics of amoebiasis with repeated acute state

Abstract

Amoebiasis is an infectious disease caused by Entamoeba histolytica and is common in regions with poor hygiene. We proposed and analyzed a modified mathematical model for the transmission dynamics of amoebiasis, which considers the possibility of a return to the acute state after a period of cyst carriage. The model shows that maintaining good hygiene practices and testing for cyst carriage can eradicate the disease. The model's basic reproduction number $ (R_0)$ is calculated, and the local and global stabilities of different model equilibria are investigated. Sensitivity analysis identifies key variables that can be controlled to govern disease transmission, and an optimal control model is shown to produce better results than models without optimal control using Pontryagin's Maximum Principle. The theoretical results are compared with the help of numerical simulations.