Models of Acquired Immunity to Malaria: A Review

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man population. The model demonstrates the impact of NAI on malaria prevalence in two

Niger villages that are entomologically and hydrologically disparate. The model suggests

that the NAI depends on hydrologically driven mosquito abundance over previous years.

Thus, greater acquired immunity is obtainable in the wet village due to more mosquito

bites as compared with the dry village. However, the model also shows how NAI dampens

the effect of increased biting, since without the effects of immunity, the wet village would

have much higher prevalence than the dry village.

5.2.9.3

Effect of population dynamics on immunity acquisition

The assumption of maintaining a constant population size, made in most models for

simplicity, needs to be addressed since it’s unclear if it matters or not, even though it seems

to be artificial. It is known that human population is characterized by birth, mortality and

immigration. Some modelers believe that the consideration of these factors in the mod-

els entails a more realistic modeling of the acquisition of immunity with time since for

instance, malaria is an endemic disease which has a high mortality rate [72], [46], [48],

[109]. Moreover, the interaction between the vector and human populations instigates a

considerable level of variability on especially the mosquito populations for which the as-

sumption of constant population may not be realistic [46].

Ngwa and Shu [46] developed a SEIR model which assumes density dependent death

rates in both the human and mosquito populations, with the total populations varying with

time. Chitnis [49], [48] on the other hand, developed a model with constant immigration

for the Susceptible class such that people enter the latter class either by birth or through

immigration. To account for population dynamics, age-specific fertility and mortality rates

are calculated for each individual and an additional mortality component, specific for each

individual (such as malarial related death), is incorporated in an individual-based malaria

risk assessment model [109]. The model demonstrated the creation of individual disease

history (immunity, infectedness and illness) depending on their circulation behavior (e.g

going to work, traveling) and residence over a given period of time. The model in[103]

includes the variability of both the human and mosquito population; the former, through

yearly census and the later, either measured directly through landing catches or estimated

based on the variability in meteorological conditions (rainfall and temperature).

Some of these models produced results which show the impact of including demo-

graphic effects in predicting the rate of fatalities that could arise from the disease. Incor-

porating population variability of humans might seem pointless in cases where the quan-

titative influence of human population growth is small enough to neglect and deserves far

less attention. However, most models considered mostly the human population dynamics

with little emphasis on the dynamics of the vector population [109], [110] which is the

major driver of malaria transmission. The emphasis on the mosquito population dynamics

dates back from the work of Ross [95]. His work suggests that if the vector population can

be reduced to below a certain threshold, then malaria can be successfully eradicated. This

threshold is typically dependent on biological factors such as the biting rate and vectorial

capacity Table (5.2) which solely depends on the vector population dynamics. In [40], the