A delayed vector-borne disease model is formulated to investigate the effect of a partial protection of the human population on the epidemic extinction. This model depicts the situation of the self protection of the population or protection conducted by a government when an epidemic outbreak occurs. The global properties of the model are completely defined, the partial protection-induced reproduction number Rp of the model is computed and we show that when Rp 1, we established that the disease will persist, and the unique positive equilibrium is globally asymptotically stable. The relation between the isolation rate and the basic reproduction number is derived to investigate the minimal protection force needed to face the infection. In the case, when the government failed to achieve the required force protection to reduce the value of Rp below 1, we derived the sensitivity of the positive equilibrium with respect to the isolation rates to determine the influence that have isolation on the epidemic final size. Finally, some numerical illustrations with their epidemiological relevance are presented.

Delay · Mathematical model · Vector-borne disease · Protection · Stability · Numerical simulations