Yusuf Fuad, Dimas Maulana, Yuliani Puji Astuti
Tuberculosis (TB) is an infectious disease caused by the Mycobacterium tuberculosis which most commonly attacks the lungs. In 2017, ten million people contracted TB and 1.6 million people died of TB. It is estimated that one million children suffering from TB and 230,000 children die due to TB, including children who die both TB and HIV. Global estimation show that there are ten million TB cases which are equivalent to 133 cases per hundred thousand population numbers, the country with the highest case is India by 27%, China by 9% and Indonesia by 8%. Some research related to the mathematical model of the spread of TB, for example the S-E-I/L model by Soyoung, the S-L-I/J-T model by Zhang, and the S-L-I-T model by Trauer. In this research proposal we will reconstruct a two-level model of the spread of tuberculosis infection, which means that this tuberculosis infection attacks two populations simultaneously, namely adult and individual children. The model used is the S-E-I-R/S-E-I-R model. The first individual who is attacked, in this case is an adult individual, then infects the individual child. Later, we obtain the disease free equilibrium which is {equation presented}. © Published under licence by IOP Publishing Ltd.
Mathematics Department, Universitas Negeri, Surabaya, Indonesia
