Mathematical model of an SEIQV Epidemic and the use of homotopy analysis method on its solution

Abstract

The health and socioeconomic risks posed by severe and sudden epidemics of infectious diseases have drawn a significant attention due to their enormous threats to human health. In order to effectively defend against them, this work modified an SEIQV epidemic model with quarantine and vaccination strategy developed by Liu and Yang [1]. Using our model, we proved the positivity of solutions and then obtained the basic reproduction number for determining whether the disease dies out completely or not. The global stabilities of disease-free equilibrium was proved, and determined by the basic reproduction number. The impact of different parameters of this model is studied. Furthermore, very accurate non perturbative, semi-analytical solutions for the non-linear equations in our epidemic model are obtained by using the Homotopy Analysis Method (HAM). Simulation results show that the number of susceptible, infected and vaccinated individuals is consistent with theoretical analysis (See attached graphs) and the results are presented and discussed quantitatively to illustrate the solution. A satisfactory agreement between theoretical and numerical results is noted (As shown in Fig 3.5a and 3.5b). The model provides a theoretical foundation for controlling and forecasting the epidemic.