# 2018 Annual Meeting of the Society for Mathematical Biology & the Japanese Society for Mathematical Biology

8-12 July 2018
Australia/Sydney timezone

## Vector feeding preference annihilates backward bifurcation and reduces endemicity

12 Jul 2018, 12:00
30m
New Law School/--101 (University of Sydney)

### New Law School/--101

#### University of Sydney

300
Oral Presentation Minisymposium: Population heterogeneity and disease spread, Mathematical Epidemiology subgroup

### Speaker

Dr Rocio Marilyn Caja Rivera (University of Notre Dame)

### Description

We propose and analyze a mathematical model of a vector-borne disease that includes vector feeding preference for carrier hosts and intrinsic incubation in hosts. Analysis of the model reveals the following novel results. We show theoretically and numerically that vector feeding preference for carrier hosts plays an important role for the existence of both the endemic equilibria and backward bifurcation when the basic reproduction number $R_0$ is less than one. Moreover, by increasing the vector feeding preference value, backward bifurcation is eliminated and endemic equilibria for hosts and vectors are diminished.

Therefore, the vector protects itself and this benefits the host. As an example of these phenomena, we present a case of Andean Cutaneous Leishmaniasis (ACL) in Peru. We use parameter values from previous studies, primarily from Peru to introduce bifurcation diagrams and compute global sensitivity of $R_0$ in order to quantify and understand the effects of the important parameters of our model. Global sensitivity analysis via partial rank correlation coefficient (PRCC) shows that $R_0$ is highly sensitive to both sandflies feeding preference and mortality rate of sandflies.

### Primary authors

Dr Rocio Marilyn Caja Rivera (University of Notre Dame) Dr Ignacio Barradas (CIMAT)

### Presentation Materials

There are no materials yet.