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

immune status of the population was viewed as a function of the vectorial capacity (Table

5.2), which drives incidence of infection in humans. However, MacDonald [143] on the

other hand demonstrated that reducing the number of mosquitos would have little effect

on the epidemiology of malaria in endemic areas. This, in fact, depends on the extent of

reduction.

5.2.10

Summary of modelling approaches

In this review, the epidemiological models of NAI to malaria have been grouped in

terms of the realism of immunity acquisition scenarios accounted for. This idea is engen-

dered by the assumption that more realistic models would boost the understanding of how

immunity effects transmission dynamics at both the individual and population level. These

models range from deterministic to ABMs and they have played substantial roles in devel-

oping epidemiological understanding of the disease. Considering that the mechanisms of

natural acquisition of immunity to malaria are so complex, the discussion of both the deter-

ministic and ABMs depends apparently on the scope of the questions asked. For instance

in [42], the earlier model of the full course of parasitemia in non-immune individual [31]

was restricted to the first wave of parasitemia in same persons. By so doing, the description

of acquired immunity was simplified, reducing it to a single dimension, with no distinction

between variant-specific and variant-transcending immune response and also ignoring de-

cay of immunity.

Compartmental SEIR models, in general, are not sufficient for reproducing the real dy-

namics of malaria as they allow only a limited account of the complex process of malaria

transmission, and NAI in particular. They make clearly artificial assumptions that seem to

make them conceptually compelling, but are actually inefficient. One considerable reason

is that malaria modelling requires an indepth study of in-host parasite dynamics rather than

a mere presence or absence of infection and prevalence in a group of population. Again,

the important sources of heterogeneity, spatial and temporal scales of transmission remain

inadequately addressed using deterministic models. A general interest for the deterministic

models is geared at knowing if one infection in one person in an entire parasite population

across an entire endemic setting will varnish or persist in a population. This is usually as-

sessed by computing the R0, which is somewhat governed by immunity status, since most

of these models assume that an individual’s probability of infecting a mosquito reduces as

immunity increases. In the deterministic models, immunity is either included by consider-

ing a separate human immune class (R_h) [51], [50],[75], [19], [39], [48], [49],[47], [46],

[43], [44] , [40] or by integrating an immunity function in existing models [59], [53], [52],

[55], [57], [58].

Agent-based models of malaria transmission, however, have become an attractive alter-

native in the evolution of malaria models in recent times. This is because they allow sim-

ulation of heterogeneous communities subjected to more realistic transmission scenarios

and can incorporate complex and stochastic issues affecting malaria spread. Thus, any kind

of heterogeneity (such as heterogeneous intervention measures, host movement, multiple

parasite variants) and stochasticity (such as inter-patient variability in duration of infection