Impacts of Vaccination and Behavior Change in the Optimal Intervention Strategy for Controlling the Transmission of Tuberculosis

Conference paper
Part of the CIM Series in Mathematical Sciences book series (CIMSMS, volume 2)


A dynamical model of TB for two age groups that incorporate vaccination of children at birth, behavior change in adult population, treatment of infectious children and adults is formulated and analyzed. Three types of control measures (vaccination, behavior change and anti-TB treatment strategies) are applied with separate rate for children and adults to analyze the solution of the controlled system by using the concept of optimal control theory. It is indicated that vaccination at birth and treatment for both age groups have impact in reducing the value of the reproduction number (\(\mathcal{R}_{o}\)) whereas behavior modification does not have any impact on \(\mathcal{R}_{o}\). Pontryagin’s Minimum Principle has been used to characterize the optimal level of controls applied on the model. It is shown that the optimal combination strategy of vaccination, behavior change and treatment for the two age groups can help to reduce the disease epidemic with minimum cost of interventions, in shorter possible time.


Optimal Control Problem Reproduction Number Infected Child Infectious Individual Basic Reproduction Ratio 
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This work is in part supported by the Swedish International Science Program (ISP) at the Department of Mathematics, Addis Ababa University.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsMizan-Teppi UniversityTeppiEthiopia
  2. 2.Department of MathematicsAddis Ababa UniversityAddis AbabaEthiopia

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