Vector-borne transmission on a landscape

Field: epidemiology · Zoo name: vector_borne · Module: modelly.zoo.vector_borne.model

Hosts live on the cells of a landscape grid and move to a random neighbouring cell with probability move per day; each is susceptible, infectious or recovered. Mosquitoes live in the cells too, m per host on average (times a per-cell habitat suitability), and are susceptible, exposed (the extrinsic incubation) or infectious. Every day a mosquito survives with probability survival and bites a times, each time a random host of its cell. An infectious bite infects a susceptible host with probability b; a bite on an infectious host infects a susceptible mosquito with probability c. New mosquitoes emerge to keep the density at m.

How it is written

Mosquitoes in the same cell and state are interchangeable, so they are a CohortTable with one row per (cell, state): survival, infection and incubation are binomial draws per row. Hosts are agents with Column arrays for their state and cell row, placed by row with CellIndex.track and moved with CellIndex.random_neighbor. A habitat raster, for example the values of a modelly.space.geo.RasterLayer, sets where the mosquitoes are: VectorScenario(habitat=...).

from modelly.zoo.vector_borne.model import VectorBorne, VectorScenario

model = VectorBorne(VectorScenario(rng=42, m=2.0))
model.r0()  # Ross-Macdonald R0
model.run()  # stops when the infection is gone
model.attack_rate()

Parameter	Default	Meaning
width, height	10, 10	landscape size in cells
hosts_per_cell	20	hosts per cell at the start
habitat	None	per-cell suitability scaling the vector density, shape (width, height)
m	2.0	mosquitoes per host
a	0.3	bites per mosquito per day
b, c	0.5, 0.5	transmission probability per bite, mosquito to host and host to mosquito
survival	0.9	daily survival of a mosquito
incubation	0.1	daily probability that an exposed mosquito becomes infectious
recovery	0.1	daily probability that an infectious host recovers
move	0.3	daily probability that a host moves to a neighbouring cell
initial_infected	10	infectious hosts at the start
steps	600	maximum run length of run()

Validation

The Ross-Macdonald reproduction number, host to host over one full cycle, is R0 = m a^2 b c P / (recovery (1 - survival)), where P is the probability that an infected mosquito survives the extrinsic incubation; r0() computes it for the discrete daily cycle of the model. It is linear in the vector density m.

tests/zoo/test_vector_borne.py runs vector densities 0.5, 2 and 4 (R0 about 0.5, 2.1 and 4.3) with three seeds, and checks for every seed that the attack rates come out in the order of R0, that the subcritical outbreak stays under 5 % (its expected size is about 1 %), and that R0 = 4 infects over 80 % of the hosts. Spatial structure keeps the attack rates below the well-mixed final size. It also checks that the habitat raster confines the mosquitoes, that hosts are conserved, and that the same seed gives the same epidemic curve.

References

• Ross, R. (1911). The Prevention of Malaria, 2nd ed. John Murray.

• Macdonald, G. (1957). The Epidemiology and Control of Malaria. Oxford University Press.

Start a project from it with modelly zoo copy vector_borne my_vector_model.