A Semi-Analytical Study on Non-Linear Differential Equations in Typhoid Fever Disease

Typhoid infection dynamics is proposed in this work. The homotopy analysis method is used to solve the relevant equations, producing the approximate analytical solutions for the four compartments, such as Susceptible \((S)\), Exposed \((E)\), Infected \((I)\) and Recovered \((R)\). The numerical simulation is utilised using a Matlab programme. In addition, the problem's numerical simulation is provided. A comparison between the numerical simulation and the analytical solution reveals excellent agreement. A number of other parameters are also discussed and graphically represented, such as the rate of innate dying \(\psi\), the rate of human recruitment (birth) \(\varphi\), the rate of disease interaction \(\alpha\), the rate of unprotected symptoms \(\tau\), the rate of infectious recovery \(\theta\), the rate at which humans who have recovered lose temporary immunity \(\sigma\), and the total number of people who die from illness \(\delta\) in the compartment of Susceptible \((S)\), Exposed \((E)\), Infected \((I)\) and Recovered \((R)\). The homotopy analysis technique is employed to solve SVEIR, SEIR, SIR, and SVEIHR.