Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection
There is significant disagreement in the epidemiological literatureregarding the extent to which reinfection of latently infected individuals contributes to the dynamics of tuberculosis (TB) epidemics. In this study wepresent an epidemiological model of Mycobacterium tuberculosis infection thatinclud...
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AIMS Press
2004-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.81 |
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| author | Benjamin H. Singer Denise E. Kirschner |
| author_facet | Benjamin H. Singer Denise E. Kirschner |
| author_sort | Benjamin H. Singer |
| collection | DOAJ |
| description | There is significant disagreement in the epidemiological literatureregarding the extent to which reinfection of latently infected individuals contributes to the dynamics of tuberculosis (TB) epidemics. In this study wepresent an epidemiological model of Mycobacterium tuberculosis infection thatincludes the process of reinfection. Using analysis and numerical simulations,we observe the effect that varying levels of reinfection has on the qualitativedynamics of the TB epidemic. We examine cases of the model both withand without treatment of actively infected individuals. Next, we consider avariation of the model describing a heterogeneous population, stratified by susceptibility to TB infection. Results show that a threshold level of reinfectionexists in all cases of the model. Beyond this threshold, the dynamics of themodel are described by a backward bifurcation. Uncertainty analysis of theparameters shows that this threshold is too high to be attained in a realisticepidemic. 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. |
| format | Article |
| id | doaj-art-853b0709f8a346759699f340914c47e5 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2004-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-853b0709f8a346759699f340914c47e52025-01-24T01:46:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182004-02-0111819310.3934/mbe.2004.1.81Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfectionBenjamin H. Singer0Denise E. Kirschner1Department of Microbiology and Immunology, The University of Michigan Medical School, Ann Arbor, MI 48109-0620Department of Microbiology and Immunology, The University of Michigan Medical School, Ann Arbor, MI 48109-0620There is significant disagreement in the epidemiological literatureregarding the extent to which reinfection of latently infected individuals contributes to the dynamics of tuberculosis (TB) epidemics. In this study wepresent an epidemiological model of Mycobacterium tuberculosis infection thatincludes the process of reinfection. Using analysis and numerical simulations,we observe the effect that varying levels of reinfection has on the qualitativedynamics of the TB epidemic. We examine cases of the model both withand without treatment of actively infected individuals. Next, we consider avariation of the model describing a heterogeneous population, stratified by susceptibility to TB infection. Results show that a threshold level of reinfectionexists in all cases of the model. Beyond this threshold, the dynamics of themodel are described by a backward bifurcation. Uncertainty analysis of theparameters shows that this threshold is too high to be attained in a realisticepidemic. 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.https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.81tbreinfectionheterogenous populations.backward bifurcationepidemicr0 |
| spellingShingle | Benjamin H. Singer Denise E. Kirschner Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection Mathematical Biosciences and Engineering tb reinfection heterogenous populations. backward bifurcation epidemic r0 |
| title | Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection |
| title_full | Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection |
| title_fullStr | Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection |
| title_full_unstemmed | Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection |
| title_short | Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection |
| title_sort | influence of backward bifurcation on interpretation of r 0 in a model of epidemic tuberculosis with reinfection |
| topic | tb reinfection heterogenous populations. backward bifurcation epidemic r0 |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.81 |
| work_keys_str_mv | AT benjaminhsinger influenceofbackwardbifurcationoninterpretationofr0inamodelofepidemictuberculosiswithreinfection AT deniseekirschner influenceofbackwardbifurcationoninterpretationofr0inamodelofepidemictuberculosiswithreinfection |