A state-time epidemiology model of tuberculosis: Importance of re-infection

[Display omitted] ► State-time model can improve upon SEIR models. ► State-time captures important re-infection effects. ► Re-infection recycles individuals into high-transmission-risk phase. ► Increased diagnosis must coincide with increased treatment adherence. An epidemiological model is presented that considers five possible states of a population: susceptible (S), exposed (W), infectious (Y), in treatment (Z) and recovered (R). In certain instances transition rates (from one state to another) depend on the time spent in the state; therefore the states W, Y and Z depend on time and length of stay in that state - similar to age-structured models. The model is particularly amenable to describe delays of exposed persons to become infectious and re-infection of exposed persons. Other transitions that depend on state time include the case finding and diagnosis, increased death rate and treatment interruption. The mathematical model comprises of a set of partial differential and ordinary differential equations. Non-steady state solutions are first presented, followed by a bifurcation study of the stationary states.