On the dynamics of a class of multi-group models for vector-borne diseases

Abstract

Abstract. The resurgence of vector-borne diseases is an increasing public health concern, and there is a need for a better understanding of their dynamics. For a number of diseases, e.g. dengue and chikungunya, this resurgence occurs mostly in urban environments, which are naturally very heterogeneous, particularly due to population circulation. In this scenario, there is an increasing interest in both multi-patch and multigroup models for such diseases. In this work, we study the dynamics of a vector borne disease within a class of multi-group models that extends the classical Bailey-Dietz model. This class includes many of the proposed models in the literature, and it can accommodate various functional forms of the infection force. For such models, the vector-host/host-vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases. Under the assumption that the contact network is strongly connected, we can define the basic reproductive number R 0 and show that this system has only two equilibria: the so called disease free equilibrium (DFE); and a unique interior equilibrium-usually termed the endemic equilibrium (EE)-that exists if, and only if, R 0 > 1. We also show that, if R 0 ≤ 1, then the DFE equilibrium is globally asymptotically stable, while when R 0 > 1, we have that the EE is globally asymptotically stable.

Multi-patch and multi-group epidemic models: a new framework

“…In short, we address how group heterogeneity, or groupness, patch heterogeneity, or patchiness, mobility patterns and behavior each alter or mitigate disease dynamics. In this sense, our paper is a direct extension of [7,8,9,12] but also other studies that capture dispersal through Lagrangian approaches -in which it is possible to track host movement after the interpatch mixing - [15,26,38,39] and a recent paper [19] that investigates the effects of daily movements in the context of Dengue.…”

Global analysis of multi-host and multi-vector epidemic models

“…The global stability of the strongly equilibrium relies on a carefully constructed Lyapunov functions and tools of graph theory, à la [17,18,23]. The uniqueness and the global stability of the strongly endemic equilibrium requires the irreducibility of the host-vector network (Theorem 3.2 and Theorem 3.3), leading to the conclusion that the disease either dies out or persists in all hosts and all vectors.…”

“…Hence, to finish the proof, we will prove that the sum S 1 + S 2 is definite-negative. To do so, we look at the coefficients of the sums from the graph-theoretical standpoint, following the same approach as [17][18][19]23]. Indeed, let G(N ) be the directed graph that represents the connectivity N between the m hosts (including the l stages) and p vectors.…”

On the dynamics of dengue virus type 2 with residence times and vertical transmission

“…is called the host-vector network configuration [38]. The result of local asymptotic stability if R 2 0 < 1 and instability if R 2 0 > 1 has been established in [71].…”