The clearance of tuberculosis infection shows an elimination of infectious Mycobacterium tuberculosis (Mtb) pathogens and infected macrophage cells. The evidence shows the existence of individuals, who are still tested negative in tuberculin skin test after living with people with active tuberculosis for up to six months. Since the Mtb pathogen is spread from person to person through airborne particles, we build a continuous-time Markov chain (CTMC) model to describe the initial infection with small amount of inhaled bacteria. The CTMC model successfully simulates sample paths presenting disease clearance. We apply the theory of multitype branching processes to analytically approximate the probability of disease clearance. We also estimate the disease clearance time, which is as less than a month for R0∈[1,1.5]. Our results demonstrate that the host immune factors affect both the probability and the time of the disease clearance. These relationships are linked by the basic reproduction number R0. Our findings provide new mechanisms for disease prevention and therapy developments.
- Continuous-time Markov chain
- Disease clearance
- In-host tuberculosis model
- Multitype branching processes