Yang Hyun M, Raimundo Silvia M
UNICAMP-IMECC, Departamento de Matemática Aplicada, Praça Sérgio Buarque de Holanda, 651, CEP: 13083-859, Campinas, SP, Brazil.
Theor Biol Med Model. 2010 Nov 8;7:41. doi: 10.1186/1742-4682-7-41.
In order to achieve a better understanding of multiple infections and long latency in the dynamics of Mycobacterium tuberculosis infection, we analyze a simple model. Since backward bifurcation is well documented in the literature with respect to the model we are considering, our aim is to illustrate this behavior in terms of the range of variations of the model's parameters. We show that backward bifurcation disappears (and forward bifurcation occurs) if: (a) the latent period is shortened below a critical value; and (b) the rates of super-infection and re-infection are decreased. This result shows that among immunosuppressed individuals, super-infection and/or changes in the latent period could act to facilitate the onset of tuberculosis. When we decrease the incubation period below the critical value, we obtain the curve of the incidence of tuberculosis following forward bifurcation; however, this curve envelops that obtained from the backward bifurcation diagram.
为了更好地理解结核分枝杆菌感染动态中的多重感染和长潜伏期，我们分析了一个简单模型。由于关于我们所考虑的模型，文献中已充分记录了向后分岔现象，我们的目的是根据模型参数的变化范围来说明这种行为。我们表明，如果：（a）潜伏期缩短至临界值以下；以及（b）重复感染和再感染率降低，向后分岔就会消失（并出现向前分岔）。这一结果表明，在免疫抑制个体中，重复感染和/或潜伏期的变化可能促使结核病发病。当我们将潜伏期缩短至临界值以下时，我们得到了向前分岔后结核病发病率的曲线；然而，这条曲线包络了从向后分岔图中得到的曲线。
