A mathematical model of Typhoid Fever disease dynamics with drug resistant aspect

Abstract

Vincent Kyunguti Mwanthi¹, Dr. Stephen Karanja², Dr. Loyford Njagi³, Prof. Mark Kimathi⁴

1. Meru University of Science & Technology

           Email: mwanthiv@gmail.com

          Phone number:   07238430778                               

1. Department of Mathematics

           Meru University of Science & Technology 

          Email: skaranja@must.ac.ke

          Phone number:0723520493                 

1. Department of Mathematics

Meru University of Science & Technology

Email: loyfordnjagi@gmail.com

            Phone number:  0723101835                                    

1. 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