Models of Acquired Immunity to Malaria: A Review

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the patient, than on the origin of the strains used (origin in this context is defined based on

the common assumption that in each region, malaria has a character of its own conferred

upon it by the peculiarities of the local parasites [141]). This, to a large extent, renders the

concept of discrete and independent strain inconsequential. Thus, the concept of malaria

parasite strains should instead be understood as variants of a given plasmodium species,

since they are dynamic entities resulting from the interaction between parasite genomes

and the human immune system [42], [76], [164], [138].

Milligan and Downham [70] demonstrated how increase in the number of circulating

strains in a population results to slower rate of reduction in susceptibility. Individuals are

considered to be immune to infection with strain k, if they have experienced at least Nk

infections with that strain after say, W bites from infected vectors. In a simple case where

vectors can host at most one parasite strain, and infection with different strains in a single

contact are mutually exclusive, the multinomial distribution can be employed while sum-

ming over different strains. Hence, the probability of getting infected with any strain at the

(W +1)th infectious bite is given as

P(W) =

s

X

k=1

qk

min(W,Nk−1)

X

r=0

W

r

!

q^r

k^{(1−qk)W−r,}

(5.2)

where qk is the probability that an individual acquires an innoculum of strain k upon re-

ceiving an infection bite. For simplicity, with a constant Nk = 2 for all strains k (although

it is host dependent), and equally abundant strains (qk = 1/S for all k), the plot of P(W)

against W with 3 different numbers of circulating strains, S is given in Figure 5.4.

The above demonstration can only be appropriate if malaria variants are discrete and

immutable as applicable in some viruses. Based on the current understanding of malaria

parasite variants, it follows that exposure to more diverse variants would progressively

reduce the repertoire of parasites clones that may be capable of establishing patent and

virulent infections [140], [88].

However, it is possible for a primary infection with a given parasite species to confer

protection against a secondary infection with heterologous species if the species share

Figure 5.4: Probability of getting infected at the (W + 1)th bite from an infectious vector

when assuming mutually exclusive strains.