Transmission Dynamics and Control Mechanisms of Vector-Borne Diseases with Active and Passive Movements Between Urban and Satellite Cities

The Big Bang of an epidemic: a metapopulation approach to identify the spatiotemporal origin of contagious diseases and their universal spreading pattern

In this paper, we propose a mathematical framework that governs the evolution of epidemic dynamics, encompassing both intra-population dynamics and inter-population mobility within a meta-population network. By linearizing this dynamical system, we can identify the spatial starting point(s), namely the source(s) and the initiation time of the epidemic, which we refer to as the "Big Bang" of the epidemic. Furthermore, we introduce a novel concept of effective distance to track disease spread within the network. Our analysis reveals that the contagion geometry can be represented as a line with a universal slope, for any disease type (R0) or mobility network configuration. The mathematical derivations presented in this framework are corroborated by empirical data, including observations from the COVID-19 pandemic in Iran and the US and the H1N1 outbreak worldwide. Within this framework, to detect the Big Bang of an epidemic we require two types of data: (1) A snapshot of the active infected cases in each subpopulation during the linear phase. (2) A coarse-grained representation of inter-population mobility. Also even with access to only the first type of data, we can still demonstrate the universal contagion geometric pattern. Additionally, we can estimate errors and assess the precision of the estimations. This comprehensive approach enhances our understanding of when and where epidemics began and how they spread. It equips us with valuable insights for developing effective public health policies and mitigating the impact of infectious diseases on populations worldwide.

A hybrid Lagrangian-Eulerian model for vector-borne diseases

In this paper, a multi-patch and multi-group vector-borne disease model is proposed to study the effects of host commuting (Lagrangian approach) and/or vector migration (Eulerian approach) on disease spread. We first define the basic reproduction number of the model, R 0 , which completely determines the global dynamics of the model system. Namely, ifR 0 ≤ 1 , then the disease-free equilibrium is globally asymptotically stable, and ifR 0 > 1 , then there exists a unique endemic equilibrium which is globally asymptotically stable. Then, we show that the basic reproduction number has lower and upper bounds which are independent of the host residence times matrix and the vector migration matrix. In particular, nonhomogeneous mixing of hosts and vectors in a homogeneous environment generally increases disease persistence and the basic reproduction number of the model attains its minimum when the distributions of hosts and vectors are proportional. Moreover, R 0 can also be estimated by the basic reproduction numbers of disconnected patches if the environment is homogeneous. The optimal vector control strategy is obtained for a special scenario. In the two-patch and two-group case, we numerically analyze the dependence of the basic reproduction number and the total number of infected people on the host residence times matrix and illustrate the optimal vector control strategy in homogeneous and heterogeneous environments.