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■Bio-mathematics, Statistics and Nano-Technologies: Mosquito Control Strategies

grouping people into discrete classes of infected and uninfected hosts. Thus, immunity in-

dicators should depend on the quantitative facets of infection, rather than on binary factors

(i.e either present or absent).

Elderkin et al. [146] and Aron [43] have attempted to model malaria parasite densi-

ties in response to immunity acquisition in their so called density model. The interaction

between immunity and infection is modeled by assuming that immunity increases at a

rate proportional to the density of asexual parasitemia, and in the absence of parasitemia,

immunity decreases. The density model did not capture the potential of reduced transmis-

sion to increase malaria prevalence in older age groups [43]] as was earlier demonstrated

in [44] (see Appendix 5.B). Also, these models present a collective behavior of a group,

thus, specific individual characteristics such as disease history, can not be tracked unlike

in more recent models [159], [76] [56], [205], [114], [115], [160], [161], [113]. A more

recent and detailed approach is seen in the OpenMalaria models where clinical symptoms

and immune response are functions of parasite density in an individual host [159],[76],

[214],[115], [134], [160], [114]. In those studies, empirical descriptions of within-host

asexual parasite densities are embedded in the model for infection process, enabling the

stochastic predictions of parasite densities as a function of age of infection. Moreso, the

effect of immunity to asexual blood stages was modelled by considering how the distri-

bution of parasite densities is modified in the semi-immune host [76]. They also analyzed

the relationship between asexual parasite densities and infectivity to the vector to derive a

model for the transmission to the vector [160], [114], which most models neglect.

5.2.2

Functional immunity/clinical immunity

The compartmental deterministic models mostly focus on illustrating how prevalence

and parasite densities dwindle with age at a given level of force of infection [43], [44].

Thus, they can only show that immunity develops after several years but are not efficient

to explain categorically how individuals mount a certain level of protective immunity after

each infection episode. The reason is mainly because most compartmental models address

only a single undifferentiated form of immunity [44], [62], [50], [48], [46]. However, vari-

ous types of NAI against plasmodia such as clinical immunity, anti-parasite immunity (see

Table 5.1) has been defined [31], [30], [32], [43]. For instance the model in [52] suggests

that anti-disease immunity grows faster with higher levels of infection and anti-parasite

immunity (which induces more rapid recovery from symptomatic or asymptomatic infec-

tions to undetectable infections) develops later in life. Moreso, some studies have shown

that immunity to severe malaria can be acquired after one or two episodes [98]. It has again

been observed that a single prior infection can induce detectable clinical immunity (Table

5.1) [31],[30]. This is based on the malaria therapy reinnoculation data examined by Mo-

lineaux et al. [30]. The study reveals that a second homologous (Table 5.2) inoculation

brings about a lower first local maximum density, which is now accepted to be probably

the most important effect of NAI to malaria. As a consequence, out of the 38 patients who

experienced fever after the first inoculation, only 31 had it after the second inoculation (see

also [126], [127], [128]). This is a particular instance of how individuals can be protected

from homologous variants. It does not nullify the fact that a complete protective immu-