### Mathematical Biosciences and Engineering

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

# A malaria model with partial immunity in humans

• 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, $R_0$, 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.

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

### Related Papers:

• 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.

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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