Abstract
the extent to which reinfection of latently infected individuals contributes to the dynamics of tuberculosis (TB) epidemics. In this study we present an epidemiological model of Mycobacterium tuberculosis infection that includes the process of reinfection. Using analysis and numerical simulations, we observe the effect that varying levels of reinfection has on the qualitative dynamics of the TB epidemic. We examine cases of the model both with and without treatment of actively infected individuals. Next, we consider a variation of the model describing a heterogeneous population, stratified by susceptibility to TB infection. Results show that a threshold level of reinfection exists in all cases of the model. Beyond this threshold, the dynamics of the model are described by a backward bifurcation. Uncertainty analysis of the parameters shows that this threshold is too high to be attained in a realistic epidemic. However, we show that even for sub-threshold levels of reinfection, including reinfection in the model changes dynamic behavior of the model. In particular, when reinfection is present the basic reproductive number, R(0), does not accurately describe the severity of an epidemic.
Highlights
Tuberculosis (TB), an infectious disease caused by the bacterium Mycobacterium tuberculosis, is estimated to infect one-third of the world’s population and results in nearly 3 million deaths per year [1, 2, 3]
Since initial infection is separated so dramatically in time from the development of disease, it is unclear whether the transition from latency to active disease is due to endogenous reactivation or exogenous reinfection [10, 11]
We explore whether the levels of reinfection that are necessary to influence bifurcation behavior are consistent with those expected to occur in a real epidemic, and whether subthreshold levels of reinfection modify the interpretation of R0
Summary
Tuberculosis (TB), an infectious disease caused by the bacterium Mycobacterium tuberculosis, is estimated to infect one-third of the world’s population and results in nearly 3 million deaths per year [1, 2, 3]. TB, Epidemic, backward bifurcation, reinfection, R0, heterogenous populations. B ν μ μtb βw βx = xβw βy = y βw βz = z βw pN pS = ppN rN rS = rrN ltN , ltS atN , atS
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