Effect of Birth Rate Simulation and Vaccination on Dynamics Measles Epidemic Patterns

Abstract

The purpose of this research is to get description about influence of birth rates to the epidemic dynamics pattern of measles is presented as system of nonlinear differential equations. In this case, the epidemic dynamics of measles is of the form of the SEIR model with births which is obtained from four compartments: susceptible, exposed, infectious, and recovered. Then we analyze parameter model (α) to know the influence of change of birth rates to the epidemic dynamics pattern of measles. The changes of birth rates do not alter common pattern of epidemic measles, but the number of epidemic cycle, epidemic process, oscillation process, epidemic size, and time of epidemic convergent changes significantly. If the birth rate increases so does the epidemic cycle, but the epidemic process decreases, the oscillation is faster, and epidemic size converges to higher level value. If the birth rate decreases, the number of epidemic cycle decreases, epidemic process and oscillation take a longer, the epidemic size decreases with higher variance and converges to lower value.