A tuberculosis epidemic model as a proxy for the assessment of the novel M72/AS01E vaccine

Dipo Aldila, Joseph Páez Chávez, Karunia Putra Wijaya, Naleen Chaminda Ganegoda, Gracia Monalisa Simorangkir, Hengki Tasman, Edy Soewono

Research output: Contribution to journalArticlepeer-review


Tuberculosis (TB) is a bacterial infectious disease that comes with a high mortality rate through manifesting lung damage. Understanding the TB transmission is critical to designing appropriate clinical monitoring in endemic areas with the end goal of eradication. This study brings forward a modeling framework taking into account recently known constituents in the multiplex transmission, namely slow–fast progression from de novo infection, relapse, slow–fast reinfection, treatment failure, resources limitation, and – to our current novelty – the implementation of new M72/AS01E vaccine. The model is a system of ordinary differential equations governing the evolution of six human compartments over time. The basic reproduction number of the model becomes an endemic measure driving the model trajectories around either a forward or backward bifurcation at its threshold value one. Sufficient conditions leading to the two types of bifurcation are shown to be dependent on the treatment availability. Owing to the backward bifurcation, failure to meet a threshold for the treatment leads to endemicity notwithstanding excellent contact restrictions and vaccination that bring about the basic reproduction number below one. The model responses to relevant individual parameters for straightforward controls are investigated numerically using Computational Continuation Core (COCO). Only forward bifurcations around branching points are discovered using the chosen parameter values in this study, with the directions controlled by the gradient of the basic reproduction number toward the vector of the parameters. We found that enhancing contact restrictions, reducing relapse rate via healthy lifestyles (improving immune systems), and increasing vaccination rate as well as its effectiveness are very crucial in contenting the epidemics. Furthermore, contact restrictions become a determinant to the extent where an endemic bubble via two adjacent Hopf points and a hysteresis loop may occur. There exists an infection rate within the endemic bubble at which the period of the trajectory blows up, resulting in the very slow movement around a saddle point before temporarily taking a one-time cycle and slowly confining to the point. Two-parameter continuation related to contact restrictions and vaccination helps locate regimes where different multistability modes occur, thereby addressing careful deployment of resources against counterproductive interventions and entraps between distinct endemicity levels.

Original languageEnglish
Article number107162
JournalCommunications in Nonlinear Science and Numerical Simulation
Publication statusPublished - Jun 2023


  • Bifurcation
  • M72/AS01 vaccine
  • Reinfection
  • Relapse
  • Treatment failure
  • Tuberculosis


Dive into the research topics of 'A tuberculosis epidemic model as a proxy for the assessment of the novel M72/AS01E vaccine'. Together they form a unique fingerprint.

Cite this