Multiplicity of infection

[JoRussell-IDM]

We will assert that in instances of complex infection, one infection becomes the founding dominant infection while the remaining infections are co-incident and inhibited relative to their predicted independent growth in a phase dependent manner.

Infections that are concurrent and in phase (peaks overlap with a window of days (3?), akin to constructive interference) should be discounted such that their respective parastemia sum to the maximum total parasite density that the dominant strain would have contributed independently. (something like find max that founding dominant infection would have allowed and discount its density by a fraction (x) and allow co-incident infections to attain densities that sum to (1-x). This will be most important for complex infections resulting from a single bite.

As soon as these two coincident infections are out of phase (peak index >3 days away from the preceding dominant infection peak), we have to allow for subsequent peaks of parasitemia to obtain high values given that their cresting is antigenically specific and different than the adjacent peak from the dominant infection.

When completely out of phase (peak index day of dominant infection = trough index of coincident infection akin to destructive interefence) , complex infections should follow the behavior that for the dominant strain peak day and several days afterwards there is an increased chance of clearance for inhibited infections that are at or near a troughs.

RESEARCH NOTE: is there any evidence for synchronization of antigenic waves? or is out-of-phase behavior the stable equilibrium? If no data, what makes the most sense?

In general this feature highlights the need for the model to allow for interruption, modification, or truncation of predicted shapes.

[JoRussell-IDM]

From experiments in a mouse/chabaudi model (PMID: 16224719)

We investigated multiple infection in malaria, using two pairs of genetically distinct clones of the rodent malaria Plasmodium chabaudi in mice. Clones were inoculated into mice simultaneously or 3 or 11 days apart, and population sizes were tracked using immunofluorescence or quantitative polymerase chain reaction. In all experiments, at least one of the two clones suffered strong competitive suppression, probably through both resource‐ and immune‐mediated (apparent) competition. Clones differed in intrinsic competitive ability, but prior residency was also an important determinant of competitive outcome. When clones infected mice first, they did not suffer from competition, but they did when infecting mice at the same time or after their competitor, more so the later they infected their host. Consequently, clones that are competitively inferior in head‐to‐head competition can be competitively superior if they infect hosts first. These results are discussed in the light of strain‐specific immunity, drug resistance, and virulence evolution theory.

[JoRussell-IDM]

These results suggest an inhibitory effect on new co-incident infections that could depend on both phase (relative to antigenic peaks) and age of founding infection.

The data we would need to support calibration of this effect are relative abundances of strains across longitudinal measurements with some bounded estimate of infection start times (maybe PRISM?)

[JoRussell-IDM]

From genotyped complex infections in Nanoro,

https://doi.org/10.1038/s41598-018-36493-y (https://www.nature.com/articles/s41598-018-36493-y)

Overall, parasite density did not increase with additional strains, suggesting the existence of within-host competition. Parasite density was influenced by msp1 allelic families with highest parasitaemia observed in MAD20 allelic family. However, when in mixed infections with allelic family K1, MAD20 could not grow to the same levels as it would alone, suggesting competitive suppression in these mixed infections.

"Overall, older patients exhibited lower parasite densities than younger patients, but this effect varied with the genetic composition of the isolates for the msp1 gene. There was no effect of msp1 and msp2 allelic family variation on body temperature. Haemoglobin level was influenced by msp2 family with patients harboring the FC27 allele showing lower haemoglobin level than mono-infected individuals by the 3D7 allele. This study provides evidence that P. falciparum genetic diversity influenced the severity of particular malaria symptoms and supports the existence of within-host competition in genetically diverse P. falciparum."

These results suggest a desired behavior of:

Individuals with more infections ought to be more likely to be sampled with a higher density (this claim needs to be backed up by data), but there should be no positive correlation between the complexity of a sampled infection and parasite density magnitude (consistent with intra host competition, observed in https://doi.org/10.1038/s41598-018-36493-y)

[JoRussell-IDM]

Literature targets for relationships between multiplicity of infection and age/exposure/symptomaticity:

from Felger 1999 on Tanzanian infants (https://doi.org/10.1016/S0035-9203(99)9032)

"The relationship of the number of concurrent infections (multiplicity) with age and morbidity was analysed and results were compared to those of a similar study on older children between 2 and 7 years of age, carried out in the same village at the same time. The mean of 2 infecting genotypes per positive blood sample from community surveys was low compared to that in older children, and there was no significant age-dependency of multiplicity within the first year of life. Multiplicity of infection in fever cases was also independent of age. In infants, multiplicity was positively associated with parasite density and risk of clinical malaria, in contrast to the situation in older children (>2 years). The findings help in the understanding of infection dynamics, premunition, and development of semi-immunity in malaria."

and from Smith 1999 (https://doi.org/10.1016/S0035-9203(99)90322-X )

The peak in multiplicity of infection (identified by polymerase chain reaction-restriction fragment length polymorphism of the msp2 locus) occurred in 3–7 years old children. There was a significant correlation between parasite density and multiplicity of infection in infants and young children (1–2 years of age) but not in older individuals.

and from Kiwuwa 2013 (https://doi.org/10.1007/s00436-013-3325-3) The multiplicity of infection (MOI), determined as the highest number of alleles detected within any of the four genetic loci, was significantly higher in severe than in mild malaria cases (mean 3.7 and 3.0, respectively, P = 0.002).

and from Ntoumi 1995 (PMID: 7856831) Both the overall number of fragments and the number of allelic types per carrier were markedly reduced around the age of 15 years. The number of DNA fragments decreased abruptly from an average of four per carrier before the age of 15 years to an average of two in individuals more than 15 years of age

[JoRussell-IDM]

One behavior we may want to incorporate down the line is a nuanced view of the competitive advantage of virulent strains of parasite (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1140419/figure/fig1/)

and how that may intersect with symptomaticity, severe disease and bottleneck pressures from drug treatments of various scales.

One thing I don't yet fully understand is what reasonable class of parasite is more or less virulent than another? Shouldn't it be pretty specific to pfemp1 functionality of a particular wave?

[JoRussell-IDM]

The most basic behavior:

1. Adding all concurrent infection densities during Update()

2. All current infections are subject to uniform scaling by a function that saturates at 500% of maximal density. factor = 1 + 4 / (1 + exp(0.5 * (7.5 - numberInfections))); If this logic remains, it might be useful to make the values configurable so that we could calibrate this saturating behavior to data as we find it.

Making these values {a:4, b:0.5, c:7.5} where a = (maximum density allowed-1)

b = steepness of logistic curve (marginal effect of additional strains)

c = midpoint (the value that specifies when we can expect the effect of the number of infections to saturate)

3. More complex timing/infection age dependent competitive scaling of co-incident infections to be implemented later as we bump up against constraints imposed by literature.