Budi Priyo Prawoto, Sifak Indana, Muhammad Budiyanto, Reni Kurnia Putri
Tuberculosis (TB) is a form of acute respiratory infection that affects the human respiratory tract. Prevention of the spread of TB can be done by administering vaccines to susceptible individuals. This study aims to construct and analyse the stability of the TB spread model in the presence of vaccination for adults. The constructed model contains seven subpopulations namely susceptible (S), vaccinated babies (Vb), vaccinated adults (Vd), exposed (E), infected (I), treatened (Q) and recovered (R). The stages carried out were literature studies, compiling assumptions, constructing models, finding equilibrium points, finding reproductive numbers by using NGM, analyzing the stability of the model, and numerical simulations. Two equilibrium points were obtained, namely the disease-free equilibrium point and the endemic equilibrium T0=(S,Vb,Vd,E,I,T,R)= (αμ+qμ2+μq+μθ+qθ,1-αμ+q,θ(αμ+q)μ(μ2+μq+μθ+qθ),0,0,0,0) will be asymptotically stable when θ>β(μα1+q)δ(μ+q)(δ+μ+ω1)(γ1+ω2+μ+η)-μ, otherwise the endemic equilibrium point, T1=(S*,Vb*,Ed*,I*,T*,R*), will be asymptotically stable. © 2025 Author(s).
Mathematics Departement, State University of Surabaya, Surabaya, Indonesia; Biologi Departement, State University of Surabaya, Surabaya, Indonesia; Sains Educationa Departement, State University of Surabaya, Surabaya, Indonesia; Mathemarics Educationa Departement, PGRI Adi Buana University, Surabaya, Indonesia
