Mathematical analysis of the rossmacdonald model with. The model incorporates into the classic rossmacdonald model two factors. 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 will formulate a periodic rossmacdonald model in a patchy environment and establish the threshold dynamics. 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. An almost periodic rossmacdonald model with age structure for the vector population in a patchy environment is considered. In the rossmacdonald model for malaria transmission, the total. 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. Transmission dynamics for vectorborne diseases in a. Malaria models with spatial effects semantic scholar. The model without coupling will exhibit a limit cycle with the parameters. Citeseerx document details isaac councill, lee giles, pradeep teregowda.
The temporal heterogeneity is described by assuming that some model coefficients are timeperiodic, while the spatial. 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. 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 classical model for the local transmission of vectorborne diseases is the ross macdonald model. An almost periodic epidemic model 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. Transmission dynamics for vectorborne diseases in a patchy.
A periodic epidemic model with age structure in a patchy. An almost periodic rossmacdonald model with structured vector. A mathematical model of complex networks resilience to external stress. These two issues are considered in lou and zhao 20 via a periodic reactiondi usionadvection model. Characterising submonolayer deposition via visibility graphs.
We show that the basic reproduction number of an sis patch model with stan. Proctor foundation for research in ophthalmology university of california, san francisco san francisco, ca 94143, usa. The last section gives some numerical simulations and a brief discussion of our main results and future research directions. The temporal heterogeneity is described by assuming that some model coefficients are time periodic, while the spatial. Citeseerx a periodic rossmacdonald model in a patchy. 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. Discrete and continuous dynamical systems series b, vol. Optimal seasonal timing of oral azithromycin for malaria. In chapter 3, based on the classical rossmacdonald model, we propose a periodic malaria model to incorporate the e. The temporal heterogeneity is described by assuming that some. 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.
A periodic rossmacdonald model in a patchy environment core. 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. Audio andor slides are available for talks given at the fields institute during the following events in the year july 2010 june 2011. 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. Pdf based on the classical rossmacdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial. The temporal heterogeneity is described by assuming that some model coefficients are time periodic, while the spatial heterogeneity is modeled by using a multi. Igtc graduate summer school in mathematical biology. A periodic rossmacdonald model in a patchy environment. A fragmented or patchy ecosystem is an ecological community constituted. A periodic reactiondiffusion system modelling manenvironmentman epidemics.
An introduction to the theory of competitive and cooperative systems. 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 paper, a periodic epidemic model with age structure in a patchy environment is introduced. 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. Zhao, a periodic epidemic model in a patchy environment, j. Li and zhisheng shuai, global stability of an epidemic model in a patchy environment, can. Rossmacdonald model, epidemiology, delayed model, agent based model 1. An almost periodic rossmacdonald model with structured. 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. In this form system is clearly a generalization on n patches of the classical rossmacdonald model, with dx as the migration term. A periodic disease transmission model with asymptomatic carriage and latency periods. Ruan 2014, a periodic rossmacdonald model in a patchy environment, discrete and continuous dynamical systems series b 1910, 333145.
The periodic rossmacdonald model with diffusion and advection, appl. Pcbs are also extremely persistent in the environment, with long half. The temporal heterogeneity is described by assuming that some model coefficients are timeperiodic. Ruan 2018, spatial and temporal dynamics of a nonlocal viral infection model, siam journal on applied mathematics78, 19541980. 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. On the basis of a periodic rossmacdonald model, gao et al. Oct 26, 2019 an almost periodic rossmacdonald model with age structure for the vector population in a patchy environment is considered. An introduction to the theory of competitive and cooperative systems, authorhal l. An sir epidemic model with vaccination in a patchy environment. Dec 01, 2014 a periodic rossmacdonald model in a patchy environment. Ams proceedings of the american mathematical society.
Meanfield dispersal induced synchrony and stability in an. Discrete and continuous dynamical systems series b 21. Pdf the rossmacdonald model in a patchy environment. Introduction preprint submitted to acta tropica arxiv. 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 timeperiodic, while the spatial heterogeneity is modeled by using a multi. The periodic rossmacdonald model with diffusion and advection. Fields institute 20102011 lecture audio and slides. 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. Further, we obtain the conditions under which the positive periodic solution is globally asymptotically stable. A periodic epidemic model in a patchy environment, j. Models for the effects of host movement in vectorborne. 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. 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.
Ruan s 2014 a periodic rossmacdonald model in a patchy environment. Pdf a periodic rossmacdonald model in a patchy environment. Ruan 2018, traveling wave solutions for the periodic reactiondiffusion systems, discrete. 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. Griffin, 2015 studied the effect of pulsed interventions such as mda and indoor residual spraying on the reproduction. A discussion of that model and its history is given in 35.
The version described here is similar to the one derived by 33 but there are many variations and extensions in the literature. Rui peng, asymptotic profiles of the positive steady state for an sis epidemic reactiondiffusion. Yijun lou and xiaoqiang zhao received 00 month 200x. Since ticks in larval and nymphal stages share the same host community which can harbor multiple pathogens, they may be co.
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. In this paper, a mathematical model is derived to describe the transmission and spread of vectorborne diseases over a patchy environment. Ruan 2014, a modeling approach to investigate epizootic outbreaks and enzootic maintenance of rift valley. 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. Exploring 30 years of malaria case data in kwazulu. By employing the persistence theory, we establish a threshold between the extinction and the uniform persistence of the disease. Deterministic models described by ordinary differential equations and reactiondiffusion equations are used to investigate the spatial spread of malaria be tween humans and mosquitoes. We first show that the disease spreading speed is coincident with the minimal wave speed for monotone periodic travelling waves. Network for biological invasions and dispersal research. The last section gives some numerical simulations and a brief discussion of. Modeling the effects of weather and climate change on malaria.
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