A new SIS malaria model with vector demography showing natural occurring oscillations
Miranda Teboh-Ewungkem, Mathematics, Lafayette College (November 6, 2010)
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A new way to model the dynamics of malaria transmission that takes into consideration the demography of the transmitting vector will be presented. Model results indicate the existence of nontrivial disease free and endemic steady state solutions which can be driven to instability via a Hopf bifurcation as a parameter is varied in parameter space. The model therefore captures natural occurring oscillations known to occur in the dynamics of mosquito populations and these oscillations lead to oscillations in the dynamics of malaria transmission without recourse to external seasonal forcing, a way that has been used in the past to obtain such oscillations. Possible reasons why it has been difficult to eradicate malaria will also be discussed. The discovery of these natural occurring oscillatory dynamics present a plausible framework for developing and implementing control strategies. These will be discussed.