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Original and proposed LMM settings

  • Raw data: colon separated values (ASCII file)

    • symbol parameter valori Refsori valpro Refspro LMM range literature range
    pd daily mosquito survival Martens I scheme Martens 1997a Martens II scheme Martens 1997 Bayoh-12.5%, Martens I & II, Lindsay-Birley -
    DgS standard Dg 37 °days Detinova 1962c NU - standard/dry/humid Dg 36.5-65.4 °days
    TgS standard Ts 9 °C Detinova 1962c NU - standard/dry/humid Ts 4.5-9.9 °C
    RH- Rainfall Humidity threshold NU - 10 mm - - -
    DgH humid Dg NU - 37.1 °days Detinova 1962 - -
    TgH humid Tg NU - 7.7°C Detinova 1962c - -
    DgL dry Dg NU - 65.4 °days Detinova 1962c - -
    TgL dry Tg NU - 4.5°C Detinova 1962c - -
    RR• rainfall laying multiplier 1.0 Hoshen and Morse 2004 NU - - -
    EGG number of produced mosquito eggs NU - 80 cp. table 50-200 eggs 5-290 eggs
    CAP cap to the number of egg laying mosquitoes NA - 750 - 100-2000 -
    LR0 daily larval survival (lab) NU - 0.825 cp. table 0.80-0.95 0.82-0.99
    MMA Mosquito Mature Age 14 days Jepson et al. 1948 12.0 days LR0- and pdl-table 11.0-15.0 days 11.2-27.6 days
    Ds degree-days of the sporogonic cycle length 111 °days Detinova 1962d 111 °days Nikolaev 1935 111.0-148.0 degree-days 111.0-204.4 degree-days
    Ts temperature threshold of the sporogonic cycle 18°C Detinova 1962d 16°C Detinova 1962d 14.0-18.0 14.2-19.0
    HBI Human Blood Index 0.5 Hoshen and Morse 2004 0.8 cp. table 0.5-0.9 0.0-1.0
    b mosquito-to-human transmission efficiency 0.5 Hoshen and Morse 2004 0.3 cp. table 0.1-0.5 0.01-0.50
    HIA Human Infectious Age 14 days Hoshen and Morse 2004 20 days cp. table 15-25 days 12-30 days
    r human recovery rate 0.0284 Hoshen and Morse 2004 0.0050 e.g. Molineaux and Gramiccia 1980 0.0010-0.0150 0.0015-0.0385
    GF gametocyte fraction NU - 0.5 cp. SAR in table 0.3-0.7 0.1-0.7
    c human-to-mosquito transmission efficiency 0.5 Hoshen and Morse 2004 0.2 cp. table 0.1-0.3 0.0-0.379
    tri,h added infectious humans 0.01 Hoshen and Morse 2004e 0.00 - - -
    tru,m added uninfected mosquitoes NA Hoshen and Morse 2004f 0.00 - - -
    tri,m added infectious mosquitoes 0.00 Hoshen and Morse 2004 1.01 -g 1.01 -

    Abbreviations

    symbolsymbol of the model parameter
    parametermodel parameter
    valorivalue of the original LMM setting (Hoshen and Morse 2004)
    Refsorireferences with regard to the original setting
    valprovalue of the proposed LMM setting
    Refsproreferences with regard to the proposed setting
    Dgdegree-days of the gonotrophic cycle [°days]
    Tgtemperature threshold of the gonotrophic cycle [°C]
    pdldaily larval survival (field)
    SARRatio between Sexual and Asexual parasite prevalence, i.e. the proportion of malaria parasite positive humans that are gametocytaemic [%]
    NUnot used

    Comments

    The fuzzy parameters with regard to the egg laying process and daily larval survival probabilities have yet not been specified (these are: FU0, FS1, FS2, FU2, LU0, LS1, LS2 and LU2).

    The setting of LMM allows the usage of either per-gonotrophic cycle (α) or daily mosquito survival probabilities (pd).

    a Martens (1997) states: "Relying on data reported by Boyd (1949), Horsfall (1949), and Clements & Patterson (1981), we assume a daily survival probability (pd) of 0.82, 0.90 and 0.04 at temperatures (T) of 9°, 20° and 40°C, respectively, expressed as: pd=exp[-1.0/(-4.4+1.31 T-0.03 T2)]." However, Hoshen and Morse (2004) were not using the cited relationship, i.e. the so-called Martens II scheme. In fact they derived a different polygon from the three data points: pd=0.45+0.054 T-0.0016 T2, i.e. the so-called Martens I scheme.

    b Bayoh (2004) observed the survival and mortality rates of Anopheles gambiae sensu stricto in environmental chambers at combinations of temperatures from 0 to 45°C at 5°C intervals and relative humidity's of 40%, 60%, 80%, and 100%. Using the data of these laboratory experiments and assuming an exponential model of mortality the following relationship has been computed: pd=-2.123 10-7 T5+1.951 10-5 T4-6.394 10-4 T3+8.217 10-3 T-2-1.865 10-2 T+7.238 10-1. However, vector survival is higher in captivity than in the wild (e.g. Clements and Paterson 1981) and hence pd has to be reduced. The shift-off was arbitrarily set to 12.5%. The probabilities of the Bayoh-12.5% scheme compare well with field observations. The so-called Bayoh-12.5% scheme agrees also fairly well with the mean daily survival of 84.6% found by Kiszewski et al. (2004).

    c Shlenova (1938) performed experiments on the duration of blood digestion and ovarian development in Anopheles maculipennis. Various temperature and humidity combinations were used under controlled conditions. Detinova (1962) analysed this data set and found: "The sum of degree-hours at different humidities is composed of the differences between the actual temperature at each hour and the threshold temperature, which at a humidity of 30-40% is 4.5°C; at 70-80%, 9.9°C; and at 90-100%, 7.7°C. ... The difference between the mean diurnal temperature and the threshold temperature is calculated for each 24-hour period. These differences are added until the sum of the effective temperatures at 30-40% humidity is 65.4; at 70-80%, 36.5 and at 90-100%, 37.1."

    d With regard to the temperature threshold of the sporogonic cycle Detinova (1962) firstly cites Nikolaev (1935): "Nikolaev (1935) established that the sporogony of Plasmodium vivax takes place at a temperature lower than 16°C, and of P. falciparum at a temperature of not less than 18°C."
    Moreover, Detinova (1962) refers to the method of Moshkovsky (1946) for determining the duration of sporogony: "The sum of heat in degree-days for the maturation of the sporozoites in the mosquito's body is 105°C for P. vivax, 111°C for P. falciparum and 144°C for P. malariae. To establish the possible duration of sporogony it is necessary to subtract from the mean diurnal temperature in 24 hours the estimated lowest development temperature threshold, which is equivalent to 14.5°C for P. vivax and 16°C for other species of malaria parasites, and then in sequence to add the differences obtained in order to reach the total necessary for the development of the given species of parasite."

    e Hoshen and Morse (2004) state: "The initial population is assumed to be non-infected, but new infections are being introduced at a constant low rate (trickle = 0.01 into a population of 100 every four days)."

    f Hoshen and Morse (2004) state: "In the model, a small constant trickle (trickle2) of young uninfected mosquitoes (representing a new imported population) is added to the population of maturing mosquitoes."

    g The interim LMM setting introduces the transmission of malaria by a constant trickle of infectious mosquitoes. Every ten days 1.01 new infectious mosquitoes have been added to the mosquito population. In this model version neither infectious humans nor uninfected mosquitoes are added.