Publication Date:
2014-11-22
Description:
We consider a vector–host model for the transmission dynamics of malaria with a gamma-distributed delay representing the incubation period of the disease in the vector. We analyse the impact of the delay on the steady states and their stability, and determine a threshold value for the mean delay at which the system undergoes either a transcritical or a backward bifurcation. We show that, the critical value depends on the shape parameter of the gamma distribution implying that the eradication or establishment of malaria does not depend only on the mean value of the delay but also on the shape parameter. A sensitivity analysis is performed by calculating the sensitivity index of the basic reproductive number and the endemic steady states to compare the effect of the mean delay and shape parameter on the initial disease transmission and the disease prevalence at the equilibrium. Numerical simulations are carried out to confirm the theoretical findings to investigate the impact of the delay on the prevalence of the disease.
Print ISSN:
0272-4960
Electronic ISSN:
1464-3634
Topics:
Mathematics
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