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Cited by 494

The DOI matches its Crossref record; 20 of the 20 references it cites were found in a registry or an index.

Bifurcation Analysis of a Mathematical Model for Malaria Transmission

Chitnis, Nakul, Cushing, J. M., Hyman, J. M.·2006·SIAM Journal on Applied Mathematics
DOI 10.1137/050638941
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Abstract

We present an ordinary differential equation mathematical model for the spread of malaria in human and mosquito populations. Susceptible humans can be infected when they are bitten by an infectious mosquito. They then progress through the exposed, infectious, and recovered classes, before reentering the susceptible class. Susceptible mosquitoes can become infected when they bite infectious or recovered humans, and once infected they move through the exposed and infectious classes. Both species follow a logistic population model, with humans having immigration and disease‐induced death. We define a reproductive number, $R_0$, for the number of secondary cases that one infected individual will cause through the duration of the infectious period. We find that the disease‐free equilibrium is locally asymptotically stable when $R_0 < 1$ and unstable when $R_0 > 1$. We prove the existence of at least one endemic equilibrium point for all $R_0 > 1$. In the absence of disease‐induced death, we prove that the transcritical bifurcation at $R_0 =1$ is supercritical (forward). Numerical simulations show that for larger values of the disease‐induced death rate, a subcritical (backward) bifurcation is possible at $R_0=1$.

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Metadata

Authors
Chitnis, N., Cushing, J. M., & Hyman, J. M.
Venue
SIAM Journal on Applied Mathematics
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
2006-01
Volume
67
Issue
1
Pages
24-45
ISSN
  • 0036-1399 (ISSN-L)
  • 1095-712X
DOI
10.1137/050638941
OpenAlex
W2053239897
Cited by
494
References
20
FWCI
6.21
Type
journal article
Language
en
Open access
closed

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CoChat. (2026). Citation check: Bifurcation Analysis of a Mathematical Model for Malaria Transmission. https://app.cochat.ai/papers/10.1137/050638941
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Chitnis, N., Cushing, J. M., & Hyman, J. M. (2006). Bifurcation Analysis of a Mathematical Model for Malaria Transmission. SIAM Journal on Applied Mathematics. https://doi.org/10.1137/050638941

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