A periodic rossmacdonald model in a patchy environment core. The temporal heterogeneity is described by assuming that some model coefficients are time periodic, while the spatial heterogeneity is modeled by using a multi. Characterising submonolayer deposition via visibility graphs. Since ticks in larval and nymphal stages share the same host community which can harbor multiple pathogens, they may be co. Proctor foundation for research in ophthalmology university of california, san francisco san francisco, ca 94143, usa.
An introduction to the theory of competitive and cooperative systems. Introduction preprint submitted to acta tropica arxiv. Citeseerx a periodic rossmacdonald model in a patchy. Further, we obtain the conditions under which the positive periodic solution is globally asymptotically stable.
Pdf a periodic rossmacdonald model in a patchy environment. Li and zhisheng shuai, global stability of an epidemic model in a patchy environment, can. Vectorborne diseases are caused by di erent types of parasites, including viruses and bacteria, which are transmitted by vectors as mosquitoes, sand. An epidemic model in a patchy environment with periodic coefficients is investigated in this paper. In this paper, it is pertinent to keep in mind that the parameters of the uncoupled epidemic model are selected in such a way. In this form system is clearly a generalization on n patches of the classical rossmacdonald model, with dx as the migration term. May 01, 2010 gao d, lou y and ruan s 2014 a periodic rossmacdonald model in a patchy environment, discrete and continuous dynamical systems series b, 10. The temporal heterogeneity is described by assuming that some model coefficients are timeperiodic, while the spatial heterogeneity is modeled by using a multi. The version described here is similar to the one derived by 33 but there are many variations and extensions in the literature. In this paper, a periodic epidemic model with age structure in a patchy environment is introduced. The classical model for the local transmission of vectorborne diseases is the rossmacdonald model. Ruan 2014, a periodic rossmacdonald model in a patchy environment, discrete and continuous dynamical systems series b 1910, 333145. In this work we present di erent formulations of the basic ross macdonald model together with a careful discussion of the assumptions behind each model. The last section gives some numerical simulations and a brief discussion of our main results and future research directions.
Meanfield dispersal induced synchrony and stability in an. In this paper, it is pertinent to keep in mind that the parameters of the uncoupled epidemic model are selected in such a way that population of every individual patch produces. Rossmacdonald model, epidemiology, delayed model, agent based model 1. By employing the persistence theory, we establish a threshold between the extinction and the uniform persistence of the disease. Mathematical analysis of the rossmacdonald model with. Oct 26, 2019 an almost periodic rossmacdonald model with age structure for the vector population in a patchy environment is considered. An almost periodic rossmacdonald model with age structure for the vector population in a patchy environment is considered. Discrete and continuous dynamical systems series b, vol. Dec 01, 2014 in this paper, we will formulate a periodic rossmacdonald model in a patchy environment and establish the threshold dynamics of the model in section 2 and section 3, respectively. The most general model presented is an agent based model for which arbitrary distributions for latency and infectious periods for both, host and vectors, is considered.
Rui peng, asymptotic profiles of the positive steady state for an sis epidemic reactiondiffusion. Based on the classical ross macdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. A periodic reactiondiffusion system modelling manenvironmentman epidemics. The model incorporates into the classic rossmacdonald model two factors. A periodic epidemic model with age structure in a patchy. Dec 01, 2014 a periodic rossmacdonald model in a patchy environment. For events from september 2012 onwards, plus selected events from juneaugust 2012, please see our video archive for events from other years, plus those juneaugust 2012 talks that are only available in audio format, please consult the audioslides home page. The classical model for the local transmission of vectorborne diseases is the ross macdonald model. A fragmented or patchy ecosystem is an ecological community constituted. Pdf the rossmacdonald model in a patchy environment.
In chapter 3, based on the classical rossmacdonald model, we propose a periodic malaria model to incorporate the e. In the rossmacdonald model for malaria transmission, the total. Griffin, 2015 studied the effect of pulsed interventions such as mda and indoor residual spraying on the reproduction. An almost periodic rossmacdonald model with structured vector. The temporal heterogeneity is described by assuming that some model coefficients are time periodic, while the spatial heterogeneity is modeled by using a multipatch structure and assuming that individuals. The purpose of this work is to study the spatial dynamics of a periodic reactiondiffusion epidemic model arising from the spread of oralfaecal transmitted diseases. The temporal heterogeneity is described by assuming that some model coefficients are time periodic, while the spatial.
An sir epidemic model with vaccination in a patchy environment. Based on the classical rossmacdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and. Jing li, xingfu zou, dynamics of an epidemic model with nonlocal infections for diseases with latency over a patchy environment, journal of mathematical biology, 2010, 60, 5, 645, 10. The temporal heterogeneity is described by assuming that some model coefficients are timeperiodic, while the spatial. In this paper, a mathematical model is derived to describe the transmission and spread of vectorborne diseases over a patchy environment. Exploring 30 years of malaria case data in kwazulu. An almost periodic epidemic model in a patchy environment. The temporal heterogeneity is described by assuming that some. We show that the basic reproduction number of an sis patch model with standard incidence is either strictly decreasing and strictly convex with respect to the di. A periodic rossmacdonald model in a patchy environment. Ams proceedings of the american mathematical society. Models for the effects of host movement in vectorborne.
Audio andor slides are available for talks given at the fields institute during the following events in the year july 2010 june 2011. On the basis of a periodic rossmacdonald model, gao et al. The periodic rossmacdonald model with diffusion and advection. We show that the basic reproduction number of an sis patch model with stan.
The temporal heterogeneity is described by assuming that some model coefficients are timeperiodic. Malaria models with spatial effects semantic scholar. A discussion of that model and its history is given in 35. Discrete and continuous dynamical systems series b 21.
Transmission dynamics for vectorborne diseases in a patchy. Ruan 2018, spatial and temporal dynamics of a nonlocal viral infection model, siam journal on applied mathematics78, 19541980. Deterministic models described by ordinary differential equations and reactiondiffusion equations are used to investigate the spatial spread of malaria be tween humans and mosquitoes. Ruan s 2014 a periodic rossmacdonald model in a patchy environment. A mathematical model of complex networks resilience to external stress. The last section gives some numerical simulations and a brief discussion of. These two issues are considered in lou and zhao 20 via a periodic reactiondi usionadvection model. Zhao, a periodic epidemic model in a patchy environment, j. Jing li, xingfu zou, dynamics of an epidemic model with nonlocal infections for diseases with latency over a patchy environment, journal of mathematical biology, 2010, 60, 5. Yijun lou and xiaoqiang zhao received 00 month 200x. Ruan 2014, a modeling approach to investigate epizootic outbreaks and enzootic maintenance of rift valley. Ruan 2018, traveling wave solutions for the periodic reactiondiffusion systems, discrete and continuous dynamical systems 38, 43294351. The periodic rossmacdonald model with diffusion and advection, appl.
Optimal seasonal timing of oral azithromycin for malaria. On the basis of the simple rossmacdonald model, it considers a model both the incubation period in the disease circle of hosts and vectors, especially on the latency of the malaria in mosquito vectors. Based on the classical rossmacdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. Gao d, lou y and ruan s 2014 a periodic rossmacdonald model in a patchy environment, discrete and continuous dynamical systems series b, 10. In this paper, we present a malaria transmission model with periodic birth rate. Pcbs are also extremely persistent in the environment, with long half. In this paper, we will formulate a periodic rossmacdonald model in a patchy environment and establish the threshold dynamics. In this paper, we will formulate a periodic rossmacdonald model in a patchy environment and establish the threshold dynamics of the model in section 2 and section 3, respectively. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Fields institute 20102011 lecture audio and slides. Network for biological invasions and dispersal research.
Ruan 2018, traveling wave solutions for the periodic reactiondiffusion systems, discrete. Igtc graduate summer school in mathematical biology. Transmission dynamics for vectorborne diseases in a. Ticks, including the ixodes ricinus and ixodes scapularis hard tick species, are regarded as the most common arthropod vectors of both human and animal diseases in europe and the united states capable of transmitting a large number of bacteria, viruses and parasites. An almost periodic rossmacdonald model with structured. Daozhou gao, yijun lou and shigui ruan, a periodic rossmacdonald model in a patchy environment, discrete and continuous dynamical systems series b, 19, 10, 33, 2014. Modeling the effects of weather and climate change on. The model without coupling will exhibit a limit cycle with the parameters. A periodic epidemic model in a patchy environment, j. We first show that the disease spreading speed is coincident with the minimal wave speed for monotone periodic travelling waves.
566 162 1113 438 1461 670 1406 1330 439 378 648 249 1080 513 1291 747 562 11 443 994 1001 140 259 1371 1139 265 740 916 386 278 541 598 402