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

Abstract

We consider the dynamics of a mosquito-transmitted pathogen in a multipatch 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.

Multi-patch and multi-group epidemic models: a new framework

“…This approach allows a more targeted control strategy for public health benefit. Therefore, the model follows a Lagrangian approach and generalize [7,9,15,26,38,39].…”

“…In short, we address how group heterogeneity, or groupness, patch heterogeneity, or patchiness, mobility patterns and behavior each alter or mitigate disease dynamics. In this sense, our paper is a direct extension of [7,8,9,12] but also other studies that capture dispersal through Lagrangian approaches -in which it is possible to track host movement after the interpatch mixing - [15,26,38,39] and a recent paper [19] that investigates the effects of daily movements in the context of Dengue.…”

Vector-borne diseases models with residence times – A Lagrangian perspective

“…Dye and Hasibeder [25,33] models involve n host and m vector patches under the assumption that only the vectors move. The models in [18,58,64], have incorporated residence times explicitly but their modeling does not account for the effective patch population size. In fact, in [18,58], the pattern of movement between patches does not produce any "net" change on the total population per patch at any given time.…”

“…A Lagrangian perspective considers the movement of individuals across patches in a framework where the hosts' origin or identity are never lost. This approach, useful in the study of the role of movement of individuals in highly connected settings albeit it has received limited attention [18,25,36,58,64].The concept of Langragian and Eulerian approaches were implemented by Okubo et al [52,51] in modeling the diffusion and aggregation of animal populations in ecology. This nomenclature has been used in the context of epidemic models by Cosner et al[18].…”

“…A Lagrangian perspective considers the movement of individuals across patches in a framework where the hosts' origin or identity are never lost. This approach, useful in the study of the role of movement of individuals in highly connected settings albeit it has received limited attention [18,25,36,58,64].…”