Vector-borne disease risk indexes in spatially structured populations

There are economic and physical limitations when applying prevention and control strategies for urban vector borne diseases. Consequently, there are increasing concerns and interest in designing efficient strategies and regulations that health agencies can follow in order to reduce the imminent impact of viruses like Dengue, Zika and Chikungunya. That includes fumigation, abatization, reducing the hatcheries, picking up trash, information campaigns. A basic question that arise when designing control strategies is about which and where these ones should focus. In other words, one would like to know whether preventing the contagion or decrease vector population, and in which area of the city, is more efficient. In this work, we propose risk indexes based on the idea of secondary cases from patch to patch. Thus, they take into account human mobility and indicate which patch has more chance to be a corridor for the spread of the disease and which is more vulnerable. They can also indicate the neighborhood where hatchery control will reduce more the number of potential cases. In order to illustrate the usefulness of these indexes, we run a set of numerical simulations in a mathematical model that takes into account the urban mobility and the differences in population density among the areas of a city. If i is a particular neighborhood, the transmission risk index TR_i measures the potential secondary cases caused by a host in that neighborhood. The vector transmission risk index VTR_i measures the potential secondary cases caused by a vector. Finally, the vulnerability risk index VR_i measures the potential secondary cases in the neighborhood. Transmission indexes can be used to give geographical priority to some neighborhoods when applying prevention and control measures. On the other hand, the vulnerability index can be useful to implement monitoring campaigns or public health investment.Comment: 16 pages, 5 figure

Investigating HLB control strategies using Genetic Algorithms: A two-orchard model approach with ACP Dispersal

This study focuses on the use of genetic algorithms to optimize control parameters in two potential strategies called mechanical and chemical control, for mitigating the spread of Huanglongbing (HLB) in citrus orchards. By developing a two-orchard model that incorporates the dispersal of the Asian Citrus Psyllid (ACP), the cost functions and objective function are explored to assess the effectiveness of the proposed control strategies. The mobility of ACP is also taken into account to capture the disease dynamics more realistically. Additionally, a mathematical expression for the global reproduction number ($R_{0}$) is derived, allowing for sensitivity analysis of the model parameters when ACP mobility is present. Furthermore, we mathematically express the cost function and efficiency of the strategy in terms of the final size and individual $R_{0}$ of each patch (i.e., when ACP mobility is absent). The results obtained through the genetic algorithms reveal optimal parameters for each control strategy, providing valuable insights for decision-making in implementing effective control measures against HLB in citrus orchards. This study highlights the importance of optimizing control parameters in disease management in agriculture and provides a solid foundation for future research in developing disease control strategies based on genetic algorithms

Modelado y análisis de redes evolutivas

"En el presente trabajo estudiamos una red bajo dos procesos simultáneos de cambio: por una parte cada nodo es considerado un sistema dinámico y por otra parte, la estructura de la red evoluciona a lo largo del tiempo. Proponemos tres modelos de evolución estructural en los cuales, la dinámica de cambio de la estructura es interpretada como un sistema dinámico. En particular, nosotros nos basamos en el formalismo de las Autónomas Celulares y de los Sistemas Conmutados para definir las características de dicho sistema. Concerniente al análisis, realizamos la demostración de dos teoremas donde exponemos las condiciones para la estabilidad del estado sincronizado en una red dinámica bajo evolución estructural. Traducimos el problema de la estabilidad del estado sincronizado a un problema de desigualdades matriciales que involucran una matriz positiva definida y la matriz de acoplamiento. La base de nuestro análisis es el teorema de la función común de Lyapunov para sistemas conmutados.""In this work we study a network under two simultaneous dynamical processes: in the one hand each node is considered as a dynamical system and, on the other, the network structure evolves over time. We propose three structural evolution models where the dynamical change of the structure is interpreted as a dynamical system. In particular, we use the Cellular Automata formalism and Switching Systems theory in order to define the features of such dynamical system. With respect to their analysis, we propose two theorems were the synchronization stability conditions for a dynamical network under structural evolution are given. We traduce the stability problem of the synchronization state to a matrix inequalities problem involving a positive define matrix and the coupling matrix. Our analysis is based on the common Lyapunov function theorem for switching systems.

Synchronization in complex networks under structural evolution

"We investigate the effects of structural evolution on the stability of synchronized behavior in complex networks. By structural evolution we mean processes that change the topology of the network. In particular, we consider structural evolution as two simultaneous processes: on one hand, the topology changes according to an arbitrary switching law among a set of admissible patterns of connection; on the other hand, the strength of connection evolves according to an adaptive law. Our results show that by constraining the admissible patterns of connection, and using an adaptive law based on the difference between the nodes, we can guarantee the stability of the synchronized solution of the network despite structural changes. Additionally, we extend our results by considering alternative structural evolution processes, namely, a node-based adaptive strategy and a resetting switching law. We illustrate our results with numerical simulation.

Dynamics of the infected population system-wide with control applied in different patches.

<p>(a) In a fully connected network the vector transmission index <i>VTR</i>_<i>i</i> is greater in patch 2. (b) In a Barabasi-Albert network the patch with largest vector transmissibility is number 4 as indicated by its <i>VTR</i>_<i>i</i>. The most effective strategy at the beginning of the outbreak is to reduce the carrying capacity in the patch with greatest <i>VTR</i>_<i>i</i>.</p

Schematic draw of a metapopulation network with human mobility.

<p>At the right we represent the measure of the Transmission Risk index <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.e008" target="_blank">(2)</a> and, at the left, we represent the Vulnerability Risk index <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.e010" target="_blank">(4)</a>.</p

Description and estimated value of the model parameters ([30, 31]).

<p>Description and estimated value of the model parameters ([<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.ref030" target="_blank">30</a>, <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.ref031" target="_blank">31</a>]).</p

Time series of the model (8)–(12) for different values of the carrying capacity <i>C</i>, and the parameters values given in Table 1 with <i>β</i> = 0.67.

<p>Time series of the model <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.e020" target="_blank">(8)</a>–<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.e024" target="_blank">(12)</a> for different values of the carrying capacity <i>C</i>, and the parameters values given in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.t001" target="_blank">Table 1</a> with <i>β</i> = 0.67.</p

Time series of the multiple patch connected according to the dwell-time matrix <i>P</i>_{<i>e</i>.<i>g</i>.1} given in (19).

<p>Time series of the multiple patch connected according to the dwell-time matrix <i>P</i>_{<i>e</i>.<i>g</i>.1} given in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.e037" target="_blank">(19)</a>.</p