Abstract:
:We incorporate a vector-bias term into a malaria-transmission model to account for the greater attractiveness of infectious humans to mosquitoes in terms of differing probabilities that a mosquito arriving at a human at random picks that human depending on whether he is infectious or susceptible. We prove that transcritical bifurcation occurs at the basic reproductive ratio equalling 1 by projecting the flow onto the extended centre manifold. We next study the dynamics of the system when incubation time of malaria parasites in mosquitoes is included, and find that the longer incubation time reduces the prevalence of malaria. Also, we incorporate a random movement of mosquitoes as a diffusion term and a chemically directed movement of mosquitoes to humans expressed in terms of sweat and body odour as a chemotaxis term to study the propagation of infected population to uninfected population. We find that a travelling wave occurs; its speed is calculated numerically and estimated for the lower bound analytically.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Chamchod F,Britton NFdoi
10.1007/s11538-010-9545-0subject
Has Abstractpub_date
2011-03-01 00:00:00pages
639-57issue
3eissn
0092-8240issn
1522-9602journal_volume
73pub_type
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