80

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

with exposure is poorly understood. The epidemiological data in the Garki project [63]

showed that the prevalence of gametocytes in areas of high transmission decreases more

rapidly with age as compared to asexual parasites. This was viewed to directly result from

increasing immunity against the pool of asexual parasites, leaving fewer to survive to pro-

duce gametocytes [185], [182], [183]. The question on whether NAI lowers survival of

circulating gametocytes was considered by Diebner et al. [32] in a model comparison pa-

per. The fits to the data on individual courses of parasitemia improved upon changing a

constant mortality rate of gametocyte to one which grows with time. However, better fits

were obtained when gametocyte mortality was allowed to grow with its age. This is in ac-

cordance with the concept of allowing gametocyte density to decline by natural mortality

[146], [43]. This amounts to the fact that immunity is geared mainly against the asexual

blood stages. In this line, some models implicitly predict infectiousness as a function of

blood-stage parasite densities without invoking any acquisition of TBI [192], [114], [160].

On the other hand, children have usually been thought to mostly contribute to trans-

mission of parasites to vectors due to their higher parasite densities [157]. Nevertheless,

studies that have examined the contributions of different ages of human hosts to the in-

fectious reservoir have found that adults also make a significant contribution (see [175],

[114], [184]). The reason could probably be because: first, the body size of adults exposes

them more frequently to mosquito bites [205]. Second, parasite densities decrease with

age and exposure as a result of immunity in a somewhat exponential manner (i.e it never

gets sterile) which can still allow infections to persist without symptoms. These reasons

suggest why onward transmission to mosquitos is plausible in adults. Boundi et. al. [174]

studied TBI in relation to age, gametocyte density and transmission intensity. It was found

that there was no relationship between TBI indicators and age, but a trend of increasing

values as gametocytaemia increases was noticed, and regarded as a confusing factor. This

seem to confirm the assumption that TBI does not apparently increase with age, and that

adaptive immune responses to gametocytes are not of epidemiologic significance. These

conclusions however, are based on insufficient evidence.

5.2.3.2

Increase in recovery rate/Decrease in infection duration

Most models considered increase in recovery rate as an indicator of immunity (see

[122], [41], [189], [40], [72], [63]), [43], [44]. Based on Macdonald’s report in [143] im-

munity is generally assumed to be proportional to the duration of infection, which results

to a formula in which the basic reproductive number is proportional to infection duration.

The model by Dietz [40] for instance, comprises two classes of humans with low and high

recovery rates, which is associated with low and high immunity levels. The concept that

NAI increases the rates of termination of infections in humans has been the subject of ex-

tensive debate. Acquired immunity is markedly known to increase with age, thus, infection

duration may be expected to decrease as immunity rises. Again, it was expected that the

decrease in parasite densities resulting from the acquisition of immunity, would lead to a

decrease in detectability with age, which would also bring about an increase in recovery

rate. Bekessy et. al. [41] in their catalytic model applied to microscopy data, observed that

for the first 4 months of life, the durations of infection were very short, and much longer in