Models of Acquired Immunity to Malaria: A Review

■79

nity can take several more episodes to achieve a sufficiently diverse repertoire of antigenic

memory which can take considerable number of years to effect depending on the transmis-

sion intensity [159], [205], [100], [63], [52], [34].

Considering that protective immunity against blood-stage infection is achieved in a

progressive manner and is never complete, a person might be free from clinical diseases

without complete loss of infection, thus posing a barrier to total disease eradication [206],

[95], [117], [150], [114], [160], [163], [130], [53]. Such chronic, sub-acute infections are

characteristics of the widely used misnomer, “asymptomatic” malaria infections which

have been recognized to result from partial immunity [117], [193] (see Table 5.1). In the

theoretical sense, from the point of view of deterministic modelling approach, the humans

in the so-called “recovered compartment” are still partially immune and can be infectious

(see [40], [57], [160]). Thus, such compartmental models of malaria transmission with

partial immunity to reinfection have noticed a phenomena called backward bifurcation(see

Table 5.2), such that two steady states exists for a given value of R0, [93], [94], [151].

This is what Smith et al. [154] referred to as the sticky situation (see the diagrammatic

illustration in [154]). The numerical simulations reveal that increasing the rate of partial

protection of recovered individuals engenders increase in the region of backward bifurca-

tion. Thus, the prevalence of malaria in African countries and the evasiveness of complete

control was linked to people with partially acquired immunity [16]. Such people do not

visit the hospital either due to being asymptomatic or having uncomplicated clinical man-

ifestations. This situation needs to be considered in planning for intervention measures.

From the view point of premunition (see Table 5.1), sterile immunity is never achieved.

Thus, a more realistic modelling would entail a proper measure of infectivity in relation

to the host disease and state, and also linking the infectivity of human to that of mosquito

infection [102], [114]. Given that most deterministic models, especially those that consid-

ered immunity and infectiousness as being binary, could not include this concept in their

models, some other deterministic compartmental models have done a related study in this

regard [103], [52]. For instance, the human population in [103] was classified into five dif-

ferent classes: susceptible to infection S1, exposed E, infected symptomatic and infectious

I1, infected asymptomatic and infectious I2, recovered but could be potentially infectious

to mosquitos S2. Although these models are advanced as compared to the binary models, in

practice infectivity is not a collective characteristics of a group but varies with individuals,

based on their parasite densities. As such, it requires an individual-based model which can

study the relationship between asexual parasite densities and infectivity to mosquito [160],

[114].

5.2.3

Unfounded assumptions about what protective efficacy of immunity constitutes

5.2.3.1

Transmission-blocking immunity (TBI)

Most models of malaria transmission assume that complete TBI can be acquired after

repeated exposure or with age [63], [40].This does not seem to be right because of the

following reasons. First, the concept that gametocyte mortality increases with host-age or