The Ross–Macdonald model in a patchy environment

Auger, Pierre; Kouokam, Etienne; Sallet, Gauthier; Tchuenté, Maurice; Tsanou, Berge

doi:10.1016/j.mbs.2008.08.010

Cited by 70 publications

(66 citation statements)

References 37 publications

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“…From an example, we have shown how to de�ne public health policies to in�uence or even eliminate a disease that spreads out. is last result has already been highlighted in [33] in the context of a vector-born transmission disease. In addition, we have made a global sensitivity analysis, allowing us to accurately determine the parameters most in�uencing the asymptotic dynamics represented by 0 .…”

Section: Discussionmentioning

confidence: 75%

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Disease Control in Age Structure Population

Kouokam

Zucker²,

Fondjo

et al. 2013

ISRN Epidemiology

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We combine the Leslie model and its derivatives with the classical compartmental SIRS models to build a model of transmission of infected diseases, in a population of hosts, whether opened or closed systems. We calculate the basic reproductive rate R 0 . Under certain conditions, when 0 < 1, there is a disease-free equilibrium that is locally asymptotically stable. In contrast, when 0 > 1, this equilibrium is unstable. en, through an example, we show how we can de�ne public health strategies to tackle an endemic. �inally we carry a global sensitivity analysis based on this basic reproduction rate to exhibit the most in�uential parameters of our model that are applied to in�uenza.

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Section: Discussionmentioning

confidence: 75%

“…Another track will be to complete our model in order to extent it to more age groups and other compartmental models, such as SEIR or SEIRS [13,34,35]. Finally the effect of spatialization in such models can be investigated as it has been done in [33,34].…”

Section: Discussionmentioning

confidence: 99%

Disease Control in Age Structure Population

Kouokam

Zucker²,

Fondjo

et al. 2013

ISRN Epidemiology

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“…Even the same disease may be modelled with very different structures (Figure 1). In the case of malaria, Koella & Antia (2003) published SIRS models incorporating resistance to drug therapy and super-infection, Yang (2000); Yang & Ferreira (2000) incorporated socioeconomic and environmental factors into SEIR models for hosts and vectors (incorporating dynamics in an SEI model for mosquitoes), Torres-Sorando & Rodriguez (1997) included migration and visitation in an SIS model and Auger et al (2008) extended the Ross-Macdonald model to several patches in a meta-population compartmental model (Ross, 1911;Mandal et al, 2011).…”

Section: Compartment Models In Epidemiologymentioning

confidence: 99%

Sensitivity to model structure: a comparison of compartmental models in epidemiology

et al. 2016

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Compartmental models have provided a framework for understanding disease transmission dynamics for over 100 years. The predictions from these models are often policy relevant and need to be robust to model assumptions, parameter values and model structure. A selection of compartmental models with the same parameter values but different model structures (ranging from simple structures to complex ones) were compared in the absence and presence of several policy interventions to assess sensitivity to model structure. Models were fitted to data to assess if this might reduce this sensitivity. The compartmental models produced wide-ranging estimates of outcome measures but when fitted to data, the estimates obtained were robust to model structure. This finding suggests that there may be an argument for selecting simple models over complex ones, but the complexity of the model should be determined by the purpose of the model and the use to which it will be put.

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“…This is in contrast to the more popular Eulerian approach, where individuals are not assigned to a particular patch, but instead simply move around between the various patches at certain prescribed rates. Examples of the Eulerian approach can be found in various contexts related to the spread of infectious diseases such as in [1,2,5,11], and are not restricted to malaria. Our methods can be used to study similar patched Ross-Macdonald models based on the Eulerian approach, but to keep our analysis concise, we restrict ourselves to models based on the less frequently used Lagrangian approach.…”

Section: Introductionmentioning

confidence: 99%

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

Ruktanonchai

Smith

Leenheer

2016

Mathematical Biosciences

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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.

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The Ross–Macdonald model in a patchy environment

Cited by 70 publications

References 37 publications

Disease Control in Age Structure Population

Disease Control in Age Structure Population

Sensitivity to model structure: a comparison of compartmental models in epidemiology

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

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