MATHEMATICAL MODELLING AND ANALYSIS OF MEASLES DISEASE.

Abstract Despite the fact that an effective vaccination is available, the measles sickness still exists in various regions of the world. With a greater than 90% attackingrate, measles is not only a health but also an economic problem as it spread very quickly leading to a lot of persons seeking medical help. This calls for ongoing research to perhaps eliminate the disease's spread by instituting hospitalization as a method of treatment. A deterministic ordinary differential equation model for the transmission dynamics of measles was formulated. The basic reproduction number (R_0) was computed using the method of the next generation matrix (NGM). The model equilibrium results are obtained, while the stability is investigated. Numerical simulation was carried out using a classical fourth order Runge-kutta method in MATLAB to illustrate the theoretical analysis. From the simulations, we investigated and established that the disease will continue to be prevalent in our society irrespective of the rate of vaccination, as long as the contact rate between susceptible humans, infectious humans and contaminated surfaces is not properly controlled and reduced to a negligeable degree. it was equally established that the enormity of measles can be remarkably rock-bottom to a negligible degree with the adoption of vaccination to control the transmission of morbillivirus.