TY - JOUR
T1 - Disease clearance of tuberculosis infection
T2 - An in-host continuous-time Markov chain model
AU - Zhang, Wenjing
N1 - Funding Information:
The author acknowledges the generous support from Simons Foundation , award no. A21-0013-001 . The author thanks Dr. Leif Ellingson from Texas Tech University for his help with language editing. The author also thanks all referees for their comments and suggestions, which are very helpful for improving the manuscript.
Publisher Copyright:
© 2021
PY - 2022/1/15
Y1 - 2022/1/15
N2 - 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.
AB - 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.
KW - Continuous-time Markov chain
KW - Disease clearance
KW - In-host tuberculosis model
KW - Multitype branching processes
UR - http://www.scopus.com/inward/record.url?scp=85114031631&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2021.126614
DO - 10.1016/j.amc.2021.126614
M3 - Article
AN - SCOPUS:85114031631
VL - 413
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
M1 - 126614
ER -