The Impact of Isolation of Identified Active Tuberculosis Cases on the Number of Latently Infected Individuals

  • Schehrazad Selmane
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6786)

Abstract

Isolation, quarantine, disinfection, inoculation, education have been the five important preventive control measures used to control an epidemic. Isolation, which is aimed at restricting the spread to susceptibles by restricting the movements of infectious cases, tops the list. Identifying and isolating patients with active tuberculosis could be effective as control measure. In order to minimize the transmission of the disease and to break the transmission chain of the Mycobacterium tuberculosis and thus the sterilization of the source of infection, we consider an optimal control strategy associated with isolation of infectious individuals who spread the disease. The existence of an optimal control for an objective functional that takes into account both the number of infectious individuals and the cost of isolation strategy, the characterization of the optimal control, and the uniqueness of the optimality system are proved. The optimality system is solved numerically using the Forward-Backward Sweep method. The numerical results showed that isolation strategy will considerably reduce the number of latently infected individuals.

Keywords

Deterministic Model Forward-Backward Sweep Method Isolation Optimal control Pontryagin’s Maximum Principle Tuberculosis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bacaer, N., Ouifki, R., Pretorius, C., Wood, R., Williams, B.: Modeling the joint epidemics of TB and HIV in a south african township. J. Math. Biol. 28(4), 365–382 (2008)MathSciNetMATHGoogle Scholar
  2. 2.
    Castillo-Chavez, C.: Dynamical models of Tuberculosis and their applications. Mathematical Biosciences and Engineering 1, 361–404 (2004)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Lenhart, S., Workman, J.T.: Optimal control applied to biological models. In: Mathematical and Computational Biology Series. Chapman&Hall/CRC, London (2007)Google Scholar
  4. 4.
    Manuel de la lutte antituberculeuse à l’usage des personnels médicaux – Programme National de Lutte Contre la Tuberculose- MSP, Direction de la prévention- INSP, édition (2001)Google Scholar
  5. 5.
    Vynnycky, E., Fine, P.E.M.: The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of reinfection. Epidemiol. Infect. 119, 183–201 (1997)CrossRefGoogle Scholar
  6. 6.
    World Health Organization (WHO), Global Tuberculosis Control. WHO report 2010. WHO/HTM/TB/2010.7Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Schehrazad Selmane
    • 1
  1. 1.Faculty of MathematicsUniversity of Sciences and Technology Houari BoumedieneAlgiersAlgeria

Personalised recommendations