Masters Degrees ((SACEMA) South African Centre for Epidemiological Modelling and Analysis)

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    Investigating the simultaneous effect of age and temperature on the population dynamics of female tsetse flies
    (Stellenbosch : Stellenbosch University, 2011-12) Elama Ameh, Josephine; Ochigbo, Josephine Elanma; Ouifki, Rachid; Hargrove, John; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    ENGLISH ABSTRACT: Age and temperature are two factors that affect mortality in adult tsetse flies. Both are found to be very important, but the simultaneous effect of these factors on the mortality rate have not been studied. This study seeks to address this, with an application to a population of female tsetse, using a model based on partial differential equations. Adult mortality is agedependent and is modelled as the sum of two exponentials, with four parameters (coefficients of each exponential): numerical analysis of a population model with this mortality structure predicts exponential growth. Analysis of each of the parameters through parameter variation shows that two of these parameters control the mortality of the nulliparous (ages 0 − 10 days) flies only while the other two only take care of flies of mature ages. Measurement of the impact of these parameters on the mortality of tsetse of different ages by the normalized forward sensitivity index method is also carried out. This is followed by fitting the model based on the age-dependent mortality along with a constant tsetse birth rate to data representing the catches of female Glossina pallidipes at Rekomitjie Research station, Zimbabwe. Considering a three parameter adult tsetse mortality, parameter analysis shows the effect of one of the parameters to affect the mortality of flies of all ages while a second controls only the mature tsetse flies of reproductive ages. A further analysis resulted in the estimate of these parameters as functions of temperature, thereby leading to the establishment of an age and temperature-dependent adult tsetse mortality. Using data for the daily average temperature records obtained in 1981 on Antelope Island, Lake Kariba, Zimbabwe, daily changes in the pupal duration (adult tsetse birth rate) changes negatively with temperature change. Incorporating this (temperature-dependent ) birth rate into the model, together with the established age and temperature-dependent adult mortality, the adult tsetse population dynamics is explored numerically. The latter model is then fitted to population data of female Glossina morsitans morsitans obtained from the same Island and for the same period as used for the temperature data. The data suggests peak tsetse population to be in the month of July and lowest in the month of December. The first quarter of the year is predicted to be most favorable for breeding tsetse while the second, showed a period of stable growth rate and a time of tsetse abundance. In addition, the dynamics with both age and temperature showed a non-uniform daily population growth contrary to that with age effect only. This study has enhanced our understanding of tsetse population dynamics for age and temperature-dependent adult mortality with temperature-dependent pupal duration and suggests the period of tsetse abundance on Antelope Island.