Spread of pneumonia in Indonesia: Susceptible vaccinated carrier infected recovered model

Pneumonia is an infectious disease caused by microorganisms such as viruses, fungi and bacteria. This article focuses on pneumonia caused by bacteria Haemophilus influenzae type b (Hib). The purpose in this article is to formulate the susceptible vaccinated carrier infected recovered (SVCIR) model, apply the model for pneumonia in Indonesia, determine the pattern of its spread, and interpret the result of applying the model. The SVCIR model is a first order nonlinear differential equation system with the independent variable t and the dependent variables S, V, C, I and R. The SVCIR model was applied to pneumonia in Indonesia by the estimating the parameters values based on annual data for 2013–2018. Based on the application, it is known that there are still 2123586 cases of pneumonia in 2030. Therefore, based on the SVCIR model with initial values and parameters used, the target of Indonesia free of pneumonia in 2030 is estimated not to be reached and only reached in 2095. Therefore, simulation was carried out to reach Indonesia that free pneumonia by 2030. Based on the simulation, by increased vaccination rate is from α = 0.016940 to α = 2.158900 or the contact rate is decreased from β = 1.805109 to β = 0.057143 and simultaneously the vaccination rate is increased from α = 0.016940 to α = 0.033338 and decreased the contact rate from β = 1.805109 to β = 0.057706 while the other parameters have not changed the target for Indonesia to be free of pneumonia by 2030 can be achieved.