Computational modelling and optimal control of measles epidemic in human population Abstract   Measles is an awfully contagious acute viral infection. It can be fatal, causing cough, red eyes, followed by a fever and skin rash with signs of respiratory infection. In this paper, we propose and analyze a model describing the transmission dynamics of a measles epidemic in the human population using the stability theory of differential equations. The model proposed undergoes a backward bifurcation for some parameter values. Sensitivity analysis is carried out on the model parameters in order to determine their impact on the disease dynamics. We extend the model to an optimal control problem by including timedependent control variables: prevention, treatment of infected people and vaccination of the susceptible humans. In an attempt to minimize the infected people and the cost applied we design the cost functional. Next, we show that optimal control exists for the system, and the Pontryagin maximum principle is employed to characterize the continuous controls. Numerical simulation is performed to justify the analytical results and discussed quantitatively.

A Deterministic Model for Q Fever Transmission Dynamics within Dairy Cattle Herds: Using Sensitivity Analysis and Optimal Controls This paper presents a differential equation model which describes a possible transmission route for Q fever dynamics in cattle herds. The model seeks to ascertain epidemiological and theoretical inferences in understanding how to avert an outbreak of Q fever in dairy cattle herds (livestock). To prove the stability of the modelxe2x80x99s equilibria, we use a matrixtheoretic method and a Lyapunov function which establishes the local and global asymptotic behaviour of the model. We introduce timedependent vaccination, environmental hygiene, and culling and then solve for optimal strategies. The optimal control strategies are necessary management practices that may increase animal health in a Coxiella burnetiiinduced environment and may also reduce the transmission of the disease from livestock into the human population. The sensitivity analysis presents the relative importance of the various generic parameters in the model. We hope that the description of the results and the optimality trajectories provides some guidelines for animal owners and veterinary officers on how to effectively minimize the bacteria and control cost beforeduring an outbreak.