A personal overview of epidemic models for mosquito-borne infections

In this paper, we present a brief, nonexhaustive overview of the features we consider most relevant in models for mosquito-transmitted infections, comparing them with the corresponding features in models for directly-transmitted infections. In particular, we focus on the basic reproduction number $ \mathcal{R}_0 $ and its relations with the exponential growth rate, the probability of an outbreak, and the final size of the epidemic. The concept of a threshold for epidemic spread based on the basic reproduction number ($ \mathcal{R}_0 > 1 $) was first introduced by Ronald Ross for malaria. Later, the study of models for vector-transmitted infections, where the vector naturally follows a seasonal cycle, has led to a definition of $ \mathcal{R}_0 $ when model parameters are time-periodic. Host heterogeneity in attractiveness to mosquitoes leads to the counter-intuitive result that protective behaviors may increase $ \mathcal{R}_0 $; we present the assumptions behind this result, and the factors that can instead help decreasing $ \mathcal{R}_0 $.