A malaria model with partial immunity in humans

Jia Li; Jia Li

doi:10.3934/mbe.2008.5.789

Mathematical Biosciences and Engineering

2008, Volume 5, Issue 4: 789-801. doi: 10.3934/mbe.2008.5.789

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A malaria model with partial immunity in humans

Jia Li

1.
Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899

Received: 01 December 2007 Accepted: 29 June 2018 Published: 01 October 2008
MSC : 34D20, 34D23, 92D30

In this paper, we formulate a mathematical model for malaria transmission that includes incubation periods for both infected human hosts and mosquitoes. We assume humans gain partial immunity after infection and divide the infected human population into subgroups based on their infection history. We derive an explicit formula for the reproductive number of infection,

R_{0}

$R_0$ , to determine threshold conditions whether the disease spreads or dies out. We show that there exists an endemic equilibrium if

R_{0} > 1

$R_0>1$ . Using an numerical example, we demonstrate that models having the same reproductive number but different numbers of progression stages can exhibit different transient transmission dynamics.

Keywords:

Citation: Jia Li. A malaria model with partial immunity in humans[J]. Mathematical Biosciences and Engineering, 2008, 5(4): 789-801. doi: 10.3934/mbe.2008.5.789

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Abstract

In this paper, we formulate a mathematical model for malaria transmission that includes incubation periods for both infected human hosts and mosquitoes. We assume humans gain partial immunity after infection and divide the infected human population into subgroups based on their infection history. We derive an explicit formula for the reproductive number of infection, $R_0$ , to determine threshold conditions whether the disease spreads or dies out. We show that there exists an endemic equilibrium if $R_0>1$ . Using an numerical example, we demonstrate that models having the same reproductive number but different numbers of progression stages can exhibit different transient transmission dynamics.

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