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

Abstract

A two-patch mathematical model of Dengue virus type 2 (DENV-2) that accounts for vectors' vertical transmission and between patches human dispersal is introduced. Dispersal is modeled via a Lagrangian approach. A host-patch residence-times basic reproduction number is derived and conditions under which the disease dies out or persists are established. Analytical and numerical results highlight the role of hosts' dispersal in mitigating or exacerbating disease dynamics. The framework is used to explore dengue dynamics using, as a starting point, the 2002 outbreak in the state of Colima, Mexico.Mathematics Subject Classification: 92C60, 92D30, 93B07. outbreak over a million cases of DF and more than 17,000 cases of DHF [32,50]. Dengue is transmitted primarily by the vector Ae. aegypti, which is now found in most countries in the tropics and sub-tropics [35,59]. The secondary vector, Ae. albopictus, has a range reaching farther north than Ae. aegypti with eggs better adapted to subfreezing temperatures [36,50]. Differences in susceptibility and transmission of dengue infection [3,39,70] raise the possibility that some serotypes are either more successful at invading a host population, or more pathogenic, or both [41]. DENV-2 is the most associated with dengue outbreaks involving DHF and DSS cases [49,61,66,74], followed by DENV-1 and DENV-3 viruses [5,35,49]. While infection with any of the four dengue serotypes could lead to DHF, the rapid displacement of DENV-2 American by DENV-2 Asian genotype has been linked to major outbreaks with DHF cases in Cuba, Jamaica, Venezuela, Colombia, Brazil, Peru and Mexico [74,61,66,49,42,60]. A possible mechanism involved in the dispersal and persistence of DENV-2 in nature is vertical transmission (transovarial transmission) via Ae. aegypti. Prior studies were unsuccessful in demonstrating vertical transmission via Ae. aegypti [62]. However, the use of advances in molecular biology has shown that vertical transmission involving Ae. aegypti and Ae. albopictus is possible in captivity and in the wild [3,10,16,31,63]. Thus, assessing transmission dynamics and pathogenicity between the DENV-2 American and Asian genotypes' differences is one of the priorities associated with the study of the epidemiology of dengue. In short, dengue has an increasing recurrent presence putting a larger percentage of the global population at risk of dengue infection, a situation that has become the norm due to the growth of travel and tourism between endemic and non-endemic regions. The aim of this work is to better understand the impact of human mobility on dengue disease transmission, its impact on dengue dynamics, and the use mobility based strategies, an standard control measures, in reducing the prevalence of dengue infections .

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.…”

A unified activities-based approach to the modelling of viral epidemics and COVID-19 as an illustrative example

“…The limitations of the homogeneous population assumption have long been recognized and a number of works [12][13][14][15][16] aimed to address them were published, gradually evolving from a somewhat ad-hoc idea of 'superspreaders' [17,18] to a generic approach where the population is divided into an arbitrary number of groups, each with the SEIR structure, interacting in an arbitrary number of locations ('patches') [19], with the times spent by member of each group in each location characterized by a set of mixing matrices. The latter somewhat abstract approach is an extension on earlier works in this direction [20][21][22][23] where particular, more disease-specific, situation were considered. A shortcoming of the developed approach, apparent once it is reduced to its simplest variant, is that, according to it, a representative susceptible comes in contact only with one person in a given 'patch', so that the probability of coming across an infective is the ratio of the number of infectives to the total population in this patch.…”