A mathematical study on the typhoid disease model

Abstract

This work proposes the dynamics of typhoid infection. Approximate analytical solutions for the four sections, Protected (T1), Susceptible (T2), Infected (T3) as well Treated (T4) are obtained by solving the appropriate equations using the Homotopy analysis technique. A MATLAB programming is employed to perform the numerical simulation. The approximate analytical outcomes as well as the numerical simulation accord quite well with each other. Several more parameters are also covered and shown graphically, such as the natural rate of births and deaths among humans, the rates at which individuals undergoing treatment separate from the percentage of individuals with infection, enrolment rate for typhoid-protected individuals in the human section, the frequency with which people go through a temporary stage as a result of typhoid illness, and the rate at which vulnerable people get infected with typhoid fever per capita in the compartment of Protected, Susceptible, Infected and Treated. The Homotopy analysis technique is utilized to resolve first order differential equations namely SEIR(Infected -Exposed- Susceptible -Recovered),SIR(Infected -Susceptible-Recovered),and SVEIHR(Recovered -Hospitalized
-Exposed-Susceptible -Vaccinated -Infected).