Maternal Antibody Susceptible Vaccinated Infected Recovered (MSVIR) Model for Tetanus Disease and Its Applications in Indonesia

Abstract

Tetanus is caused by Clostridium tetani bacteria that infect open wounds. Tetanus infection can cause death if not treated promply. SIR models are constructed to explain the spread of infectious diseases. Tetanus is not an infectious disease, but SIR models still can be used. Infected persons can not transmit the disease through contact. Tetanus infection is affected by the environment and first aid when injured. Lack of environment and awareness in first aid will increase the case of tetanus. Prevention efforts are done by vaccination in children, women of childbearing age, and pregnant women as protection for mother and baby (maternal antibody). The purposes of this research are to formulate SIR model with vaccination and maternal antibody (MSVIR) for tetanus disease and to apply the model in Indonesia. The MSVIR model is a first order linear differential equation system with five dependent variables, there are M, S, V, I, and R, and an independent variable t (time). The parameter's values were estimated based on data in 2009-2014. The accuracy of this model was measured based on data in 2015-2016 years. The relative error rates on 2015-2016 were -0.0567 and 0.0825. The model is considered good enough. Based on the predictions during 2011-2030, the incidence of tetanus will increase 6.62% by 1.2% average increase per year.