Statistical analysis of within-host dynamics of "Plasmodium falciparum" infections

Plasmodium falciparum malaria remains one of the world’s most important infectious diseases, with at least 300 million people affected worldwide and between and 1.5 million malaria related deaths annually. The eradication program of WHO which was launched in 1955 was motivated by mathematical transmission models. However the evaluation of recent advances in malaria control (using insecticide-impregnated bednets and new therapeutic regimes such as artemesinin derivatives, combination therapy) has largely neglected the effects on transmission, and malaria transmission models have failed to capitalise on enormous advances in computing and molecular parasitology. Two important factors in models of malaria transmission are the extent of superinfection and the length of time for which clones of malaria parasites persist in the partially immune host. These determine to a large extent the likely effects of vaccines, of impregnated bed nets, and of residual spraying with insecticides on malaria transmission. The effects of acquired immunity on these quantities are also important, both in understanding transmission and the likely parasitological effects of vaccination. However the estimation of these quantities is difficult because malaria infections are often not detectable in the blood. As with many other laboratory tests used to detect infectious agents, methods for detecting malaria parasites generally have imperfect sensitivity, especially for light infections. Statistical modeling should take into account the occurrence of false negatives, otherwise naïve estimates will provide misleading information on the transition dynamics of the infection. The deterministic models in literature that made some allowance for imperfect detectability had no good way of estimating its extent
because only light microscopy was available at that time for assessment of malaria
parasitaemia in the field.
Advances in molecular typing techniques (for instance the PCR and GeneScan) and
computer-intensive statistical methods make it feasible to estimate these quantities from
field data. The goal of the present study was therefore to address the following questions:
· What is the duration of untreated malaria infections in endemic areas? How does
this vary depending on the age and exposure of the human host?
· How is the incidence of malaria superinfection in endemic areas related to age
and exposure?
· What is the detectability of the PCR
We addressed these questions using the following approaches:
Statistical analysis of data from a panel survey comprising 6 two-monthly samples from
an age-stratified cohort of 300 individuals in the Kassena-Nankana District (KND) of
Northern Ghana (an area holoendemic for P. falciparum). The msp-2 locus of the parasite
was used as a marker locus to track individual parasite clones. PCR-RFLP typing of this
locus and GeneScan using a subset of 69 individuals from this cohort provided the
genotyping data used for the analysis. We developed and fitted an immigration-death
model to this data. The model was fitted using both Maximum Likehood methods (using
the maximization algorithm in the NAG Routines implemented via the software Fortran
90) and using Bayesian inference (via MCMC simulation employing the Metropolis
algorithm in the software WinBUGS 1.4).
We also analysed data obtained for patterns of infection determined by light microscopy
in the Garki project, an intensively monitored experiment in malaria eradication in
Northern Nigeria, carried out in 1971-1977. Similarly, we analysed parasitological data
from two other eradication projects in West Papua from 1953-1955 and from the Pare-
Taveta scheme in East Africa during 1955-1966. We developed and fitted exponential
decay models to these data using WinBUGS 1.4.
In many malaria transmission models, the survival time of infections within the host is
assumed to follow an exponential distribution. The last source of data used for our
analysis is malariatherapy data from Georgia (U.S.A.) collected during 1940-1963. This
data was used to test this commonly used assumption in the literature. We fitted using
Maximum likelihood methods, four alternative statistical distributions commonly used
for survival data and compare the fits using standard statistical tests.
The main results of our findings were as follows:
Allowing for the fact that many infected people have multiple parasite clones, it was
estimated that untreated Plasmodium falciparum infections in asymptomatic individuals
residing in Navrongo will last for approximately 600 days. This result has implications
for evaluating the effect of intervention programs in endemic settings. We conclude that a
waiting time of about 2 years is needed to draw conclusions about the effectiveness of
intervention programs such as insecticide spraying, treated bednets, and mosquito source
reduction.
Using data from PCR-RFLP analysis, we estimated that the rate at which individuals
acquire new infections in the Navrongo site is on average 16 per year, while data from
the GeneScan technique gave an estimate of 19 new infections per year.
Though it is often reported that children acquire infections more often than adults, we did
not find any relationship between the infection rate and age. We could not draw any firm
conclusions from the results from our methods regarding the relationship between past
exposure and the duration of infection. However some of our results indicate a tendency
for the duration of infection to decrease with age, suggesting that as immunity increases,
there is a higher tendency to clear infections faster.
The GeneScan technique for analyzing infection dynamics has a better performance than
the PCR-RFLP. Using GeneScan, a total of 119 alleles were detected, while using the
PCR-RFLP, only 70 alleles were detected using samples from the same 69 individuals.
Using PCR genotyping data of blood samples from the 69 individuals, it was estimated
that only 47% of the alleles present in a host is detected in a finger-prick blood sample.
The best fit for the distribution of the survival time was obtained from two distributions
namely: the Weibull and the Gompertz distribution as opposed to the exponential
distribution which has been the most commonly used distribution. This suggests that
duration of Plasmodium falciparum may also depend on the age of the infection. The
results obtained here indicate that the older the infections, the faster it will be cleared.
These results also have important implications for models of malaria transmission and for
planning intervention programs. For instance if an intervention program is carried out at a
time of the year when people harbour a lot of new infections, it will require a longer
waiting period to evaluate the effect of this program. However the data used to obtain this
result was obtained from naïve individuals in non-endemic settings. We did not test this
result on data from endemic areas. It is therefore recommended that these alternative
distributions should be tested using data from endemic areas and the fits compared with
that from the exponential distribution.