Optimal control analysis of a tuberculosis model

In this paper, we extend the model of Liu and Zhang (Math Comput Model 54:836-845, 2011) by incorporating three control terms and apply optimal control theory to the resulting model. Optimal control strategies are proposed to minimize both the disease burden and the intervention cost. We prove the existence and uniqueness of optimal control paths and obtain these optimal paths analytically using Pontryagin's Maximum Principle. We analyse our results numerically to compare various strategies of proposed controls. It is observed that implementation of three controls is most effective and less expensive among all the strategies. Thus, we conclude that in order to reduce tuberculosis threat all the three controls must be taken into consideration concurrently.

Optimal control application to an Ebola model

Ebola virus is a severe, frequently fatal illness, with a case fatality rate up to 90%. The outbreak of the disease has been acknowledged by World Health Organization as Public Health Emergency of International Concern. The threat of Ebola in West Africa is still a major setback to the socioeconomic development. Optimal control theory is applied to a system of ordinary differential equations which is modeling Ebola infection through three different routes including contact between humans and a dead body. In an attempt to reduce infection in susceptible population, a preventive control is put in the form of education and campaign and two treatment controls are applied to infected and late-stage infected (super) human population. The Pontryagins maximum principle is employed to characterize optimality control, which is then solved numerically. It is observed that time optimal control is existed in the model. The activation of each control showed a positive reduction of infection. The overall effect of activation of all the controls simultaneously reduced the effort required for the reduction of the infection quickly. The obtained results present a good framework for planning and designing cost-effective strategies for good interventions in dealing with Ebola disease. It is established that in order to reduce Ebola threat all the three controls must be taken into consideration concurrently.