Habitat fragmentation promotes malaria persistence

  • Daozhou Gao
  • P. van den Driessche
  • Chris CosnerEmail author


Based on a Ross–Macdonald type model with a number of identical patches, we study the role of the movement of humans and/or mosquitoes on the persistence of malaria and many other vector-borne diseases. By using a theorem on line-sum symmetric matrices, we establish an eigenvalue inequality on the product of a class of nonnegative matrices and then apply it to prove that the basic reproduction number of the multipatch model is always greater than or equal to that of the single patch model. Biologically, this means that habitat fragmentation or patchiness promotes disease outbreaks and intensifies disease persistence. The risk of infection is minimized when the distribution of mosquitoes is proportional to that of humans. Numerical examples for the two-patch submodel are given to investigate how the multipatch reproduction number varies with human and/or mosquito movement. The reproduction number can surpass any given value whenever an appropriate travel pattern is chosen. Fast human and/or mosquito movement decreases the infection risk, but may increase the total number of infected humans.


Vector-borne disease Basic reproduction number Human movement Disease persistence Line-sum symmetric matrix Habitat fragmentation 

Mathematics Subject Classification

92D30 91D25 34K60 15B48 



The authors would like to thank the two referees for careful reading and good comments, and Drs. Linda Allen, Chao-Ping Dong, and Yang Kuang for helpful discussions.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematics and Science CollegeShanghai Normal UniversityShanghaiChina
  2. 2.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  3. 3.Department of MathematicsUniversity of MiamiCoral GablesUSA

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