Open Access Open Access  Restricted Access Subscription or Fee Access

A delay differential equation model of a vector borne disease with direct transmission

Abid Ali Lashari, Khalid Hattaf, Gul Zaman

Abstract


We formulate and systematically study the dynamics of a simple vector host epidemic model in terms of delay differential equations. The model is analyzed using stability theory of delay differential equations. Both the disease-free and the endemic equilibria are found and their stability is investigated. It is shown that the introduction of time delay in the model has a destabilizing effect on the system and periodic solutions can arise by Hopf bifurcation. Using the theory of differential and integral equation, we show that the infection free equilibrium is globally asymptotically stable if the reproductive number R0 less than 1, and the endemic equilibrium is locally asymptotically stable if R0 greater than 1.

Keywords


Vector-host model, Time delay, Stability, Hopf bifurcation.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.