Open Access Open Access  Restricted Access Subscription or Fee Access

Subharmonic Bifurcation in Malaria Epidemic Model

Akindele A. Onifade, Olawale S. Obabiyi


Seasonal variations in rainfall and resource availability are ubiquitous and can exert strong pressure on population dynamics. This study considers seasonal variation of mosquito on the transmission dynamics of malaria. The epidemic threshold parameters are computed to examine variation in the basic reproduction number. Stability of disease free and endemic equilibria with respect to seasonal variation in mosquito birth and transmission of malaria when the basic reproduction number is less or greater than unity are discussed. Applying perturbation method, stable subharmonic bifurcation solutions of period n are proved to coexist simultaneously and an infinite number of stable subharmonic bifurcation solutions are established. Numerical simulations are carried out to investigate the effects of seasonal variation of mosquito birth and transmission rate on the dynamic behavior of the system. This study suggests that intervention strategies need to be deployed especially when there is sufficient rainfall that can sustain vector development and survival. Also, every effort must be put in place by all concerned to prevent the parasite infection by reducing the basic reproduction number, until malaria eradication is achieved.


Subharmonic bifurcation, seasonal variation, Reproduction number, stability.

Full Text:


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. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.