A Mathematical Model and Analysis of an SVEIR Model for Streptococcus Pneumonia with Saturated Incidence Force of Infection
Opara Chiekezi Zephaniah, Uche-Iwe Ruth Nwaugonma, Inyama Simeon Chioma, Omame Adrew
Abstract
In this paper, the dynamics of SVEIR model with saturated incidence force of infection and saturated vaccination function for Streptococcus pneumonia (that is, model that monitors the temporal transmission dynamics of the disease in the presence of preventive vaccine) was formulated and analyzed. The basic reproduction number that determines disease extinction and disease survival was revealed. The existing threshold conditions of all kinds of the equilibrium points are obtained and proved to be locally asymptotic stable for disease-free equilibrium using linearization method and Lyapunov functional method for Endemic equilibrium. Qualitative Analysis of the model was obtained and the positive of solution obtained. It was revealed that the model is positively –invariant and attracting. Thus the region is positively invariant. Hence, it is sufficient to consider the dynamics of the model (1) in the given region. In this region, the model can be considered as been epidemiologically and mathematically well-posed. The governing model was normalized and also Adomian Decomposition method was used to compute an approximate solution of the non-linear system of differential equations governing the model. Maple was used in carrying out the simulations (numerical solutions) of the model. Graphical results were presented and discussed to illustrate the solution of the problem. The achieved results reveal that the disease will die out within the community if the vaccination coverage is above the critical vaccination proportion. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease.