An edge-based SIR model for sexually transmitted diseases on the contact network.

Sexually transmitted diseases, which are infections through sexual contact, pose severe public health threat nowadays. In this paper, we develop a novel model for such diseases on a bipartite random contact network. Our model is precise with arbitrary initial conditions, which makes it suitable to study preventative vaccination strategies. We derive the reproduction number and show that R0=1 is the disease threshold. An implicit formula for the final epidemic size is also derived, and we show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We find that the final size in either sex is heavily influenced by the degree distribution of the opposite sex.

Transmission dynamics and optimal control of a Huanglongbing model with time delay.

In this paper, a mathematical model has been formulated for the transmission dynamics of citrus Huanglongbing considering latent period as the time delay factor. Existence of the equilibria and their stability have been studied on the basis of basic reproduction number in two cases τ=0 and τ>0. The results show that stability changes occur through Hopf bifurcation in the delayed system. Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using three time-dependent control variables determined from sensitivity analysis. By using Pontryagin's Maximum Principle, we obtain the optimal integrated strategy and prove the uniqueness of optimal control solution. Analytical and numerical findings suggest that it is feasible to implement control techniques while minimizing the cost of implementation of optimal control strategies.