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      • KCI등재

        TUBERCULOSIS TRANSMISSION MODEL WITH CASE DETECTION AND TREATMENT

        Bhunu, C.P.,Mushayabasa, S.,Magombedze, G.,Roeger, L.I. The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.3

        A deterministic tuberculosis model for theoretically assessing the potential impact of the combined effects of case detection in the presence of treatment is formulated. The qualitative features of its equilibria are analyzed and it is found that the disease-free equilibrium may not be globally asymptotically stable when the reproduction number is less than unity. This disease threshold number is further used to assess the impact of active TB case finding alone and in conjunction with treatment. A critical threshold parameter ${\Theta}$ say for which case detection will have a positive impact is derived. Using the Centre Manifold theory, the model may exhibit the phenomenon of backward bifurcation (coexistence of a locally stable endemic equilibrium with a stable disease-free equilibrium) when the reproduction number is less than unity. It is shown that the possibility of backward bifurcation occurring decreases with increase case detection. Graphical representations suggest that increase in case finding accompanied by treatment of detected TB cases, result in a marked decrease of TB cases (both latent and active TB).

      • KCI등재

        TUBERCULOSIS TRANSMISSION MODEL WITH CASE DETECTION AND TREATMENT

        C. P. Bhunu,S. Mushayabasa,G. Magombedze,L.-I. Roeger 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.3

        A deterministic tuberculosis model for theoretically assessing the potential impact of the combined effects of case detection in the presence of treatment is formulated. The qualitative features of its equilibria are analyzed and it is found that the disease-free equilibrium may not be globally asymptotically stable when the reproduction number is less than unity. This disease threshold number is further used to assess the impact of active TB case finding alone and in conjunction with treatment. A critical threshold parameter Θ, say for which case detection will have a positive impact is derived. Using the Centre Manifold theory, the model may exhibit the phenomenon of backward bifurcation (coexistence of a locally stable endemic equilibrium with a stable disease-free equilibrium) when the reproduction number is less than unity. It is shown that the possibility of backward bifurcation occurring decreases with increase case detection. Graphical representations suggest that increase in case ¯nding accompanied by treatment of detected TB cases, result in a marked decrease of TB cases (both latent and active TB).

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