Investigating the combined effects of distributed delays, logistic growth and density-dependent biting rate on the dynamics of a vector borne-disease.

Abstract

We present and analyze a vector-borne disease model with two gamma distributed delays representingВ the incubation periods of the disease in the vector and hosts. The model assumes a logisticВ growth for both the host and vector populations and includes a density-dependent biting rate.

We start by highlighting the role of density dependency in the vector’s population by fitting the vector’ model to data on tsetse flies. Our fitting routine uses Bayesian based Markov Chain Monte Carlo methods and statistics comparison tests.

Then we proceed with our mathematical analysis by investigating the impact of both (distributed) delays on the model’s equilibria and their stability properties. This leads to the derivation of an explicit conditions for the occurrence of backward bifurcation, showing in the process the role of nonlinearity in the bitting rate in shaping the model’s bifurcation behavior.

Finally, a sensitivity analysis is performed by means of the forward sensitivity index of the basicВ reproductive number to compare the effect of the mean and shapeВ parameters of the delay on the initial disease transmission.