A metapopulation model for malaria with transmission-blocking partial immunity in hosts

Abstract

A metapopulation malaria model is proposed using SI and SIRS models for the vectors and hosts, respectively. Recovered hosts are partially immune to the disease and while they cannot directly become infectious again, they can still transmit the parasite to vectors. The basic reproduction number [Formula: see text] is shown to govern the local stability of the disease free equilibrium but not the global behavior of the system because of the potential occurrence of a backward bifurcation. Using type reproduction numbers, we identify the reservoirs of infection and evaluate the effect of control measures. Applications to the spread to non-endemic areas and the interaction between rural and urban areas are given.

The role of residence times in two-patch dengue transmission dynamics and optimal strategies

“…rural versus urban). The patches are coupled by a matrix whose entries represent the proportion of time that residents (under the assumption that only humans can "move") spend (or have budgeted) "visiting" another patch (Agusto, 2014;Arino et al, 2012;Cosnera et al, 2009;Sattenspiel, 2009). This twopatch model of dengue fever is an extension of the work in Carlos (2009), where a deterministic two-patch model was used to model the impact of uniderectional motions (from Patch 1 to Patch 2).…”

Genotype and spatial structure shape pathogen dispersal and disease dynamics at small spatial scales

“…Diseases are frequently aggregated across multiple spatial scales (Soper 1929, Burdon 1987. Nevertheless, while a large body of literature has explored large-scale geographical patterns (Rambaut et al 2008, Meentemeyer et al 2012, and several recent papers have studied disease dynamics in a metapopulation framework (Keeling and Gilligan 2000, Laine and Hanski 2006, Arino et al 2012, few empirical studies have focused on the patterns and mechanisms behind disease clusters at small spatial scales (''disease foci''), especially in wild host-pathogen systems. While wind-dispersed species in particular are well known for their long-distance dispersal, it is crucial to realize that the vast majority of passively dispersing spores remain airborne only a short while and land within a few meters from their source Laine 2006, Lannou et al 2008).…”

A Multipatch Malaria Model with Logistic Growth Populations

“…In particular, models of malaria in this direction include Dye and Hasibeder [13], Hasibeder and Dye [17], Torres-Sorando and Rodriguez [44], Rodriguez and Torres-Sorando [34], Smith et al [38], Auger et al [5], Cosner et al [9], Arino et al [3], etc. For references on general epidemic models in a patchy environment, we refer the reader to two review articles by Wang [46] and Arino [2].…”