Models of Acquired Immunity to Malaria: A Review

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Table 5.2: Glossary of some epidemiological terms

Basic

reproduction

number (R0)

The number of secondary cases of disease that could arise from

a single infected individual in a totally susceptible population,

over the full duration of that infection [203].

Vectorial capacity

The number of potentially infectious inoculation of another hu-

man from a single infected human, through the vector popula-

tion, per unit time [204].

Prevalence

The proportion of people affected by a disease at a point in time

[217].

Force of infection

Per capita rate of acquiring new blood-stage infection per unit

time[205].

Entomological innocu-

lation rate (EIR)

The number of infectious bites sustained by an individual over a

defined time period [66], [210]. It is the preeminent measure for

assessing malaria endemicity and transmission intensity.

Heterologous (homolo-

gous)

Having different(same) evolutionary origin [88], [30].

Backward bifurcation

A condition where a stable endemic equilibrium coincides with

a stable disease-free equilibrium when the associated reproduc-

tion number is less than one. Its epidemiological consequence

is that the conventional prerequisite of the reproduction number

being less than one becomes only necessary, but not sufficient,

for disease elimination [206].

Holoendemic

Perennial intense transmission with protective clinical immu-

nity among adults. It is the highest level of endemicity in which

the strongest level of acquired immunity is attained. Classically,

holoendemic malaria is associated with the following thresholds

for epidemiological indications in the human population: spleen-

rate of over 75% in children 2–9 years of age, and low spleen-

rate of less than 25% in adults [209].

Mesoendemic

Variable transmission that fluctuates with changes in one or

many local conditions, such as weather. It features spleen-rate

of 11–50% in children 2–9 years of age [209].

captures the basic features of the interaction between the fractions of infected human and

mosquito population. Macdonald attempted the subject of immunity to malaria, but he did

not succeed in modelling it. Again, his model is of course highly simplified since it does

not distinguish between the various infected classes of human and mosquito hosts in order

to account for the different stages of the parasite development [97].

A new deterministic malaria transmission model was developed by Dietz [40] some

years after Macdonald’s death, in which humans can gain temporary immunity. The model

has only one class “immune negatives” for the immune individuals, and at the same time

it assumed that they have no parasites in their body. It also failed to account for the loss of

immunity and stochastic phenomena that are particularly necessary when transmission is

significantly reduced. As a result, it obviously can not apply well in low endemic areas, as

demonstrated simplistically in [44]. Many other mathematical models [49], [48], [46], [62]

have also made it appear that immunity is simulated as a simple binary variable, where a