A logistic delay differential equation model for Chagas disease with interrupted spraying schedules

Abstract

This work studies a mathematical model for the dynamics of Chagas disease, a parasitic disease that affects humans and domestic mammals throughout rural areas in Central and South America. It presents a modified version of the model found in Spagnuolo et al. [A model for Chagas disease with controlled spraying, J. Biol. Dyn. 5 (2011), pp. 299-317] with a delayed logistic growth term, which captures an overshoot, beyond the vector carrying capacity, in the total vector population when the blood meal supply is large. It studies the steady states of the system in the case of constant coefficients without spraying, and the analysis shows that for given-averaged parameters, the endemic equilibrium is stable and attracting. The numerical simulations of the model dynamics with time-dependent coefficients are shown when interruptions in the annual insecticide spraying cycles are taken into account. Simulations show that when there are spraying schedule interruptions, spraying may become ineffective when the blood meal supply is large.

Media alert in an SIS epidemic model with logistic growth

“…If 1 2 ≤ p ≤ 1, both terms in the bracket of formula (22) are positive and hence det(M(E 1 )) > 0. If 0 < p < 1 2 , from Case I in Section 2 we know I 1 < I n < I e .…”

“…In fact, varying total populations were discussed before (e.g. [1,3,5,9,11,22,29,36]). Here, we assume that the population of a community follows the logistic growth.…”

A Model for the Transmission of Chagas Disease with Random Inputs

“…Section II presents the model, following [31], [32]. The sensitivity analysis in the seven chosen parameters is described in Section III.…”

“…However, there are parts of Latin America where the disease seems to be uncontrollable, such as the Bolivian Since insecticide spraying is essential in controlling the disease, there is considerable interest in optimizing the spraying schedules so as to make them as effective as possible in decreasing the domestic insect population. A basic model for the disease transmission dynamics that includes the effects of insecticide spraying was constructed and investigated in [31], and related issues were studied in [7], [9], [32]. Several applied Chagas disease transmission models have been developed, such as a deterministic model [11], a stochastic Markovian model [35], as well as a specific mathematical model to optimize spatio-temporal strategies to control the Chagas disease vectors [18].…”

“…Here, we build on the research in [32], where a modified model with a delayed logistic term in the vector equation was presented, analyzed, and issues related to spraying schedules were numerically simulated. In this work we also modify the delay-differential equation for the vector population growth by using two delays.…”