A mathematical model of Typhoid Fever disease dynamics with drug resistant aspect - MWANTHI, VINCENT KYUNGUTI; Dr. Stephen Karanja; Dr. Loyford Njagi; Prof. Mark Kimathi4, (Meru Universty of Science and Technology International Conference (MUSTIC), 2025)
Vincent Kyunguti Mwanthi1, Dr. Stephen Karanja2, Dr. Loyford Njagi3, Prof. Mark Kimathi4 Meru University of Science & Technology Email: mwanthiv@gmail.com Phone number: 07238430778 Department of Mathematics Meru University of Science & Technology Email: skaranja@must.ac.ke Phone number:0723520493 Department of Mathematics Meru University of Science & Technology Email: loyfordnjagi@gmail.com Phone number: 0723101835 Department of Pure and Applied Sciences Machakos University Email: mark.kimathi@mksu.ac.ke Phone number: 0707823927 ABSTRACT Typhoid fever continues to be a major global health challenge in the developing countries. The emergence of drug-resistant Typhoid strain currently is major problem in tackling this scourge. We propose mathematical model on dynamic transmission of Typhoid fever in human populations with antibiotic-resistant aspect and analyzes the impact of treatment using antibiotics. The model consists of human population and pathogen population. The human population is grouped into six compartments namely; susceptible individuals, exposed individuals, individuals infected with drug sensitive strain, individuals infected with drug resistant strain, recovered individuals and bacterial population. We formulated a non-linear ordinary differentials equation of the model. The control reproduction number , was derived using next-generation matrix approach and was used to analyze dynamical behavour of the disease. If the disease is contained and if it persists leading to endemic state. The local stability and a global stability analysis at disease free equilibrium points were determined using Routh-Hurwitz conditions and Lyapunov functions respectively. The disease-free equilibrium and endemic equilibrium were determined using theories of ordinary differential equations. Sensitivity analysis was done using normalized forward sensitivity index in order identify the most important model parameters. Using MATLAB, numerical simulation was done and graphs plotted. The findings indicated that effective treatment and strict hygiene practices especially when one is handling food, drinking water and beverages, is adequate to eradicate the disease in the community. KEY WORDS: Typhoid Fever, Drug resistant strain, Stability analysis, Endemic