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

single class exist for the immunes. However, in reality, protective immunity to malaria is

achieved in a progressive manner. At the initial stages of exposure, anti-disease immunity

(Table 5.1) is acquired for protection against death or severe clinical diseases, then with

more exposure to the disease at adolescent and early adulthood, immunity fights against

even milder clinical attacks. Then at mid adulthood especially in endemic areas, immunity

gives a stronger and wider range of protection against all circulating parasite variants [39],

[68], [36], [69], although sterile immunity (Table 5.1) is probably never achieved [133],

[165]. Furthermore, the mere distinction between immune and non immune is not consis-

tent with the knowledge that immunity acquisition is a dynamic process driven by trans-

mission intensity and the genetic complexity of circulating parasites (see Section 5.2.6).

Thus, some models have considered immunity as a sequence with different levels of pro-

tection, so as to evaluate the role of repeated exposure on malaria transmission dynamics

in a population [68],[40],[50], [94], [52].

The human population was classified in [103] into five different 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. The model

by Yang [50] comprises seven human compartments where the immune class is split into

three categories: immune, partially immune and non-immune but with immunologic mem-

ory. Niger and Gumel [94] also developed a deterministic malaria model which incorpo-

rates three stages of immunity. The human population comprises seven mutually exclusive

sub-populations: susceptible humans SH(t), first-time infected humans I1(t), first-time re-

covered humans R1(t), second-time infected humans I2(t), second-time recovered humans

R2(t), third-time infected humans I3(t) and third-time recovered humans R3(t). It is as-

sumed that individuals in the R3 class have the highest possible acquired immunity from

exposure, which would be long-lived. Numerical simulations illustrate that infectious indi-

viduals with their first infection transmit the disease at a higher rate as compared to those

with their second or third infections. These models demonstrated the impact of immunity

boosting on delaying the entrance of a previously infected human to the susceptible class.

They also extend some earlier malaria modelling studies by including multiple infected

and recovered human classes in an attempt to account for the effect of repeated exposure

to infection. However, it is should be taken as just an illustrative model since for instance

in [94], more repeated exposure is needed to gain immunity that can last as long as was as-

sumed for those in the R3 class in reality. Furthermore, dividing into immune and partially

immune [50] is not enough to explain the progressive pattern of immunity, but allowing

some relevant change in immune function with the age of the host would be a better alter-

native [52], [118].

In order to validate immunological markers of protection, Filipe et al. [52] developed

an age-structured malaria transmission compartmental model which combines epidemio-

logical and immunological processes. In their SEI model for the humans, there are three

classes for infected humans : infection with severe disease, asymptomatic patent infection,

and infection with undetectable parasite density. Based on the model, NAI can function

in three complementary ways: reducing the likelihood of clinical disease, accelerating the

clearance of parasite, i.e, recovery from asymptomatic to undetectable infection, and im-