Global proprieties of a delayed epidemic model with partial susceptible protection.

In the case of an epidemic, the government (or population itself) can use protection for reducing the epidemic. This research investigates the global dynamics of a delayed epidemic model with partial susceptible protection. A threshold dynamics is obtained in terms of the basic reproduction number, where for R0<1 the infection will extinct from the population. But, for R0>1 it has been shown that the disease will persist, and the unique positive equilibrium is globally asymptotically stable. The principal purpose of this research is to determine a relation between the isolation rate and the basic reproduction number in such a way we can eliminate the infection from the population. Moreover, we will determine the minimal protection force to eliminate the infection for the population. A comparative analysis with the classical SIR model is provided. The results are supported by some numerical illustrations with their epidemiological relevance.

Global dynamics of alcoholism epidemic model with distributed delays.

This paper aims to investigate the global dynamics of an alcoholism epidemic model with distributed delays. The main feature of this model is that it includes the effect of the social pressure as a factor of drinking. As a result, our global stability is obtained without a "basic reproduction number" nor threshold condition. Hence, we prove that the alcohol addiction will be always uniformly persistent in the population. This means that the investigated model has only one positive equilibrium, and it is globally asymptotically stable independent on the model parameters. This result is shown by proving that the unique equilibrium is locally stable, and the global attraction is shown using Lyapunov direct method.