Determination of the risk of malaria using different models for mosquito biting and mortality rates
Abstract
Malariais a serious and sometimes a fatal epidemic affecting nearly half of the world’s
population. In this project, we analyse a non-linear deterministic model to assess
the relation between rainfall, temperature, relative-humidity as climatic variables
and malaria incidence. The seven equations from the compartmental model were
reduced to two of which was used to derive the reproduction number as a function of
the climatic variables. We analysed both the local and global stability of the disease free
equilibrium points and also the local stability of the endemic equilibrium.
We settled on two different biting rates and two different mortality rates so as to
accommodate the different climatic variables under study. Our scope to analyse different
biting and mortality rates was achieved by simultaneously substituting two
models; one biting rate and one mortality rate into the reproduction number after
which numerical simulations are provided to determine the correlation between climatic
variables and malaria incidence.
Apart from reproduction number, the other index used in the analysis of the relation
between temperature and future risk of malaria is the epidemic potential which
showed qualitatively that an increase or decrease in temperature will lead to a corresponding
behaviour in malaria incidence. Our findings in this study confirm that
indeed there is some correlation between climatic variables and the dynamics of both
total and confirmed malaria incidence.
Publisher
University of Nairobi