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Parasite sources and sinks in a patched Ross-Macdonald malaria model with human and mosquito movement: implications for control

Parasite sources and sinks in a patched Ross-Macdonald malaria model with human and mosquito movement: implications for control
Parasite sources and sinks in a patched Ross-Macdonald malaria model with human and mosquito movement: implications for control
We consider the dynamics of a mosquito-transmitted pathogen in a multi-patch Ross–Macdonald malaria model with mobile human hosts, mobile vectors, and a heterogeneous environment. We show the existence of a globally stable steady state, and a threshold that determines whether a pathogen is either absent from all patches, or endemic and present at some level in all patches. Each patch is characterized by a local basic reproduction number, whose value predicts whether the disease is cleared or not when the patch is isolated: patches are known as “demographic sinks” if they have a local basic reproduction number less than one, and hence would clear the disease if isolated; patches with a basic reproduction number above one would sustain endemic infection in isolation, and become “demographic sources” of parasites when connected to other patches. Sources are also considered focal areas of transmission for the larger landscape, as they export excess parasites to other areas and can sustain parasite populations. We show how to determine the various basic reproduction numbers from steady state estimates in the patched network and knowledge of additional model parameters, hereby identifying parasite sources in the process. This is useful in the context of control of the infection on natural landscapes, because a commonly suggested strategy is to target focal areas, in order to make their corresponding basic reproduction numbers less than one, effectively turning them into sinks. We show that this is indeed a successful control strategy—albeit a conservative and possibly expensive one—in case either the human host, or the vector does not move. However, we also show that when both humans and vectors move, this strategy may fail, depending on the specific movement patterns exhibited by hosts and vectors.
0025-5564
90-101
Ruktanonchai, Nick
fe68cb8d-3760-4955-99fa-47d43f86580a
Smith, David L
726ac8a3-342d-4955-bd50-433e58984dc3
De Leenheer, Patrick
ec48505d-74b9-43e5-a496-a7941ec4a1bf
Ruktanonchai, Nick
fe68cb8d-3760-4955-99fa-47d43f86580a
Smith, David L
726ac8a3-342d-4955-bd50-433e58984dc3
De Leenheer, Patrick
ec48505d-74b9-43e5-a496-a7941ec4a1bf

Ruktanonchai, Nick, Smith, David L and De Leenheer, Patrick (2016) Parasite sources and sinks in a patched Ross-Macdonald malaria model with human and mosquito movement: implications for control. Mathematical Biosciences, 279, 90-101. (doi:10.1016/j.mbs.2016.06.012).

Record type: Article

Abstract

We consider the dynamics of a mosquito-transmitted pathogen in a multi-patch Ross–Macdonald malaria model with mobile human hosts, mobile vectors, and a heterogeneous environment. We show the existence of a globally stable steady state, and a threshold that determines whether a pathogen is either absent from all patches, or endemic and present at some level in all patches. Each patch is characterized by a local basic reproduction number, whose value predicts whether the disease is cleared or not when the patch is isolated: patches are known as “demographic sinks” if they have a local basic reproduction number less than one, and hence would clear the disease if isolated; patches with a basic reproduction number above one would sustain endemic infection in isolation, and become “demographic sources” of parasites when connected to other patches. Sources are also considered focal areas of transmission for the larger landscape, as they export excess parasites to other areas and can sustain parasite populations. We show how to determine the various basic reproduction numbers from steady state estimates in the patched network and knowledge of additional model parameters, hereby identifying parasite sources in the process. This is useful in the context of control of the infection on natural landscapes, because a commonly suggested strategy is to target focal areas, in order to make their corresponding basic reproduction numbers less than one, effectively turning them into sinks. We show that this is indeed a successful control strategy—albeit a conservative and possibly expensive one—in case either the human host, or the vector does not move. However, we also show that when both humans and vectors move, this strategy may fail, depending on the specific movement patterns exhibited by hosts and vectors.

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More information

Accepted/In Press date: 30 June 2016
e-pub ahead of print date: 17 July 2016
Published date: September 2016
Organisations: WorldPop, Population, Health & Wellbeing (PHeW)

Identifiers

Local EPrints ID: 401959
URI: https://eprints.soton.ac.uk/id/eprint/401959
ISSN: 0025-5564
PURE UUID: 8a06be97-f591-4024-b22c-d5c2a082d192

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Date deposited: 25 Oct 2016 13:27
Last modified: 15 Aug 2019 05:16

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