Page 254 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling

Notes Introduction

The proximate cause of malaria in a human is the presence of Plasmodium parasites, which may
appear after an infective bite by an Anopheles mosquito. The probability that parasites are
transmitted from a mosquito to a human in any given interaction necessarily depends on the
probability that parasites were transmitted from a human to that mosquito in some previous
human-mosquito interaction, which in turn depends on earlier links in the chain of transmission,
and thus on densities of infectious and susceptible humans and mosquitoes, on innate and
acquired host immunity, strains and species of parasite and vector, sea and environmental
factors, and so forth. That is, human malaria is characterized by hierarchies of dynamic processes,
occurring on diverse time scales within and between heterogeneous populations.
Here we develop models of malaria epidemiology by depicting the biology of parasite
development in individual humans and mosquitoes, and the corresponding interactions between
humans and mosquitoes. We distinguish each host and vector unit by its state within a characteristic
repertoire of states, we define a set of probabilistic interactions that may effect state transitions
in interacting units, i.e., parasite transmission, and we simulate multiple interactions among
multiple entities. This scheme requires no special computing resources, but it provides realistic
sampling processes by representing large, finite populations of individuals, and allows relatively
realistic degrees of complexity in population-level dynamics to emerge from simple, transparent
representations of individual-level malaria infections.
Such discrete-event models complement the differential-equation “compartment” models that
have made such enormous contributions to our understanding of malaria transmission. The
most influential of these models, Macdonald’s refinement of the Ross archetype, focused a
global malaria-eradication campaign on reducing adult mosquito survivorship. Though this
campaign succeeded brilliantly in many temperate and subtropical regions, it often failed
elsewhere, particularly in regions with intense perennial transmission. Macdonald published
posthumously that “a powerful tool for the design of eradication and control programs, and for
the analysis of difficulties in them, could be produced by the extension of dynamic studies using
computer techniques.” Our objectives here are to introduce a basic discrete-event simulation
model, compare its results in conditions of intense perennial transmission to those of differential-
equation models, and investigate circumstances in which the utility of such abstractions as
average individuals and infinite populations might be challenged.

Task Explain the working of basic discrete-event simulation model.
Design

Plasmodium infection of a human begins with a small inoculum of sporozoites from the salivary
glands of a blood-feeding female Anopheles mosquito. The sporozoites penetrate liver cells, and
in hepatic schizogony transform and multiply to produce thousands of free merozoites. Each of
these merozoites invades a red blood cell, completes another round of multiplication (in erythrocyte
schizogony), then bursts the cell, releasing 8 to 32 more merozoites to invade more red blood cells.
This asexual blood cycle may be repeated many times, in the course of which some invading
merozoites may instead develop into the sexual, non-replicating transmissible stages known as
gametocytes. If viable gametocytes of each sex are taken up by a feeding Anopheles, fertilization
may produce the zygotes from which infective sporozoites arise within the mosquito, in sporogony.
Our discrete-event models identify the potential states of an individual host or vector with the
sequential phases of a P. falciparum malaria infection in each such that a single variable that

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