## Optimal control for a tuberculosis model with undetected cases in Cameroon

Please always quote using this URN: urn:nbn:de:0297-zib-43142
• This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 % in 10 years

Author: Dany Pascal Moualeu, Martin Weiser, Rainald Ehrig, Peter Deuflhard ZIB-Report Tuberculosis; Nonlinear dynamical systems; Optimal control 34-XX ORDINARY DIFFERENTIAL EQUATIONS 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] 65-XX NUMERICAL ANALYSIS 2013/11/25 ZIB-Report (13-73) 1438-0064 published in Comm. Nonlin. Sci. Num. Sim. 20 (3): 986-1003, 2014. Creative Commons - Namensnennung

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