The metapopulation dynamics of an infectious disease: tuberculosis in possums.

An SEI metapopulation model is developed for the spread of an infectious agent by migration. The model portrays two age classes on a number of patches connected by migration routes which are used as host animals mature. A feature of this model is that the basic reproduction ratio may be computed directly, using a scheme that separates topography, demography, and epidemiology. We also provide formulas for individual patch basic reproduction numbers and discuss their connection with the basic reproduction ratio for the system. The model is applied to the problem of spatial spread of bovine tuberculosis in a possum population. The temporal dynamics of infection are investigated for some generic networks of migration links, and the basic reproduction ratio is computed-its value is not greatly different from that for a homogeneous model. Three scenarios are considered for the control of bovine tuberculosis in possums where the spatial aspect is shown to be crucial for the design of disease management operations.

[1]  M. Efford.  Demographic consequences of sex‐biased dispersal in a population of brushtail possums , 1998 .

[2]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[3]  G. Hess.  Disease in Metapopulation Models: Implications for Conservation , 1996 .

[4]  N. Barlow.  A model for the spread of bovine Tb in New Zealand possum populations , 1993 .

[5]  A L Lloyd,et al.  Spatial heterogeneity in epidemic models. , 1996, Journal of theoretical biology.

[6]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[7]  R. Jackson,et al.  Naturally occurring tuberculosis caused by Mycobacterium bovis in brushtail possums (Trichosurus vulpecula): II. Pathology. , 1995, New Zealand Veterinary Journal.

[8]  R. Jackson,et al.  Temporal patterns in bovine tuberculosis in a brushtail possum population contiguous with infected cattle in the Ahaura Valley, Westland. , 1999, New Zealand veterinary journal.

[9]  D. Nokes,et al.  A comparison of fertility control and lethal control of bovine tuberculosis in badgers: the impact of perturbation induced transmission. , 1997, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[10]  G. Ruxton.  The effects of stochasticity and seasonality on model dynamics : bovine tuberculosis in badgers , 1996 .

[11]  R. Pech,et al.  A model of the velocity of advance of foot and mouth disease in feral pigs , 1990 .

[12]  N. Barlow.  The ecology of wildlife disease control : simple models revisited , 1996 .

[13]  N. Barlow.  Bovine tuberculosis in New Zealand: epidemiology and models. , 1994, Trends in microbiology.

[14]  Andrew P. Dobson,et al.  Ecology of Infectious Diseases in Natural Populations. , 1996 .

[15]  A. L.,et al.  Spatial Heterogeneity in Epidemic Models , 2022 .

[16]  M. Roberts,et al.  A comparison of wildlife control and cattle vaccination as methods for the control of bovine tuberculosis , 1999, Epidemiology and Infection.

[17]  R R Kao,et al.  The dynamics of an infectious disease in a population with birth pulses. , 1998, Mathematical biosciences.

[18]  O. Diekmann,et al.  On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations , 1990, Journal of mathematical biology.

[19]  R. Jackson,et al.  Prevalence and spatial distribution of bovine tuberculosis in brushtail possums on a forest-scrub margin. , 1994, New Zealand veterinary journal.

[20]  M. Efford,et al.  THE EFFECT OF MANIPULATING POPULATION DENSITY ON THE PROBABILITY OF DEN-SHARING AMONG COMMON BRUSHTAIL POSSUMS, AND THE IMPLICATIONS FOR TRANSMISSION OF BOVINE TUBERCULOSIS , 1998 .

[21]  G. Hickling,et al.  Effects of sustained control of brushtail possums on levels of Mycobacterium bovis infection in cattle and brushtail possum populations from Hohotaka, New Zealand. , 1999, New Zealand veterinary journal.

[22]  J. Wilesmith,et al.  Tuberculosis: the disease and its epidemiology in the badger, a review , 1989, Epidemiology and Infection.

[23]  Mick G. Roberts,et al.  Mathematical models for microparasites of wildlife , 1995 .

[24]  R. Morris,et al.  Naturally occurring tuberculosis caused by Mycobacterium bovis in brushtail possums (Trichosurus vulpecula): III. Routes of infection and excretion. , 1995, New Zealand veterinary journal.

[25]  R. Morris,et al.  Directions and issues in bovine tuberculosis epidemiology and control in New Zealand. , 1995, New Zealand veterinary journal.

[26]  C. King,et al.  The handbook of New Zealand mammals , 1990 .

[27]  S. A. Levin,et al.  Ecology of Infectious Diseases in Natural Populations: Spatial Dynamics of Parasitism , 1995 .

[28]  B. T. Grenfell,et al.  Ecology of Infectious Diseases in Natural Populations: Introduction , 1995 .

[29]  O. Diekmann,et al.  Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation , 2000 .

[30]  N. Barlow,et al.  A SPATIALLY AGGREGATED DISEASE/HOST MODEL FOR BOVINE Tb IN NEW ZEALAND POSSUM POPULATIONS , 1991 .

[31]  A. Dobson,et al.  Ecology of Infectious Diseases in Natural Populations , 1996 .

[32]  Andrew P. Dobson,et al.  Ecology of Infectious Diseases in Natural Populations: Frontmatter , 1995 .

[33]  B. Grenfell,et al.  Ecology of Infectious Diseases in Natural Populations: Mathematical Models for Macroparasites of Wildlife , 1995 .

[34]  Mick G. Roberts,et al.  The Dynamics of Bovine Tuberculosis in Possum Populations, and its Eradication or Control by Culling or Vaccination , 1996 .