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

and the reduced survival of the inoculations as the hosts acquire pre-erythrocytic immunity.

This model accounted for the non-monotonic relationships between the age of the host and

risk factors such as parasite prevalence and clinical malaria. This non-monotonic relation

appears to be because the risk factors increases with age (accompanied with increasing

body size), and at the same time, immunity decreases the risks. However, while some re-

cent age-structured models have considered the concept of increasing human attractiveness

as they age, grow and increase in biomass [114], [160], others have ignored this concept

and assumed equal biting rates among individuals [6], [16], which is unrealistic.

In general, age and acquired immunity are inseparable factors that hugely determine

the disease burden in a given population, especially in endemic areas [215]. This implies

that increasing age does not itself result in immunity acquisition. Anderson and May [59]

incorporated age structure in the classical Ross model by studying the population fraction

of humans in the infected class as a function of not only time, but age as well; with the sole

aim of enabling infection in a given population to depend on the age of an individual over

time . However, upon matching the predicted dependence based on the their model with

the observed prevalence trend in [60], it was revealed that the model is not a good fit to

the data since they had not considered NAI in their model. The need to explicitly interplay

NAI with age was apparent (see [16], [38]). Furthermore, the simulation studies that do

not consider maternal antibodies or varied biting rates as a function of age, generate curves

that reach adult equilibrium levels more quickly than are observed in real data [192].

5.2.5

Duration of acquired immunity to malaria

Immunity is generally modeled based on the fact that individuals are born susceptible

and can become infected with respect to a certain rate of infection per year, h (otherwise

known as the force of infection (Table 5.2)); after which they can recover within a certain

period of time and can acquire a certain level of immunity with repeated exposure. Peo-

ple routinely exposed to malaria accumulate memory B cells specific for malaria antigens

with exposure. In most mathematical models, the duration of immunity, τ is suggested

without taking re-exposure to infection into account [59], [67], [65], [152]. This again

stems from the binary view of malaria adopted by most modellers which wrongly suggests

that there is an automatic switch between presence or absence of immunity and malaria

parasites. However, epidemiological studies have proven that this approach of describing

the duration of immunity could be unrealistic since it is observed that both blood-stage

immunity and pre-erythrocytic protection against malarial infection are boosted with ex-

posure to infection [61], [63], [76] (see next subsection for more details). Some models

considered that re-exposure could boost immunity [79], [70], [106]. Dutertre, in his model,

[64] included a discrete class of immune humans whose entrance to susceptible class is de-

layed by re-exposure, and calculated on a monthly basis. Aron in [45], again developed a

continuous-time process of immunity acquisition based on the underlying assumption that

NAI abates gradually in the absence of reinfection and suggested that immunity can last

until τ years without exposure, but if there is an exposure before the time τ elapses, the

immunity is strengthened and lasts longer. On the other hand, if immunity lasts for τ years

in the absence of new infections, then the individual becomes highly susceptible to severe