SIS and SIR epidemic models under virtual dispersal

A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R 0 is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if R 0 ≤ 1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R 0 > 1 whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness, a measure of host-vector heterogeneous structure, on the basic reproduction number R 0 , are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence.Mathematics Subject Classification: 92D30, 34D23, 34A34, 34C12 .

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“…Therefore the trace of M vh M hv is only positive eigenvalue of M vh M hv . Hence, by using (7), we obtain:…”

Section: Effects Of Heterogeneitymentioning

confidence: 99%

“…We prove that the disease free equilibrium is GAS if R 0 ≤ 1 and that a unique endemic equilibrium exists and is GAS if R 0 > 1 whenever the multipatch, multi-group system is irreducible. This approach has been used in the study of a general SIS model in the context of communicable diseases ( [7]).…”

Section: Introductionmentioning

confidence: 99%

Vector-borne diseases models with residence times – A Lagrangian perspective

Bichara

Castillo‐Chavez

2016

Mathematical Biosciences

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“…Following the approach in [41], the role of density-dependent cross-diffusion in the aggregation of individuals according to epidemiological states during a nefarious disease outbreak is carried out below. We expand on the type of cross-diffusion model in [6] via the use only of a population of S-individuals (susceptible) and I-individuals (infectives), that is, symptomatic infectious individuals. The model below assumes that symptoms generate avoidance.…”

Section: Cross-diffusion Modelsmentioning

confidence: 99%

“…The effect that aggregation of susceptible and infected populations of individuals has on the basic reproduction number, R 0 , and the final size has been studied by various researchers (see [1,2,3,6,7,16,25]). The effect of aggregation on R 0 and the final outbreak size is not necessarily the same as a small core group with a high activity level can substantially contribute to R 0 while having little impact on the final outbreak size [15].…”

Section: Introductionmentioning

confidence: 99%

From Bee Species Aggregation to Models of Disease Avoidance: The Ben-Hur effect

Yong

Herrera

Castillo‐Chavez

2016

Mathematical and Statistical Modeling for Emerging and Re-Emerging Infectious Diseases

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The movie Ben-Hur highlights the dynamics of contagion associated with leprosy, a pattern of forced aggregation driven by the emergence of symptoms and the fear of contagion. The 2014 Ebola outbreaks reaffirmed the dynamics of redistribution among symptomatic and asymptomatic or non-infected individuals as a way to avoid contagion. In this manuscript, we explore the establishment of clusters of infection via density-dependence avoidance (diffusive instability). We illustrate this possibility in two ways: using a phenomenological driven model where disease incidence is assumed to be a decreasing function of the size of the symptomatic population and with a model that accounts for the deliberate movement of individuals in response to a gradient of symptomatic infectious individuals. The results in this manuscript are preliminary but indicative of the role that behavior, here modeled in crude simplistic ways, may have on disease dynamics, particularly on the spatial redistribution of epidemiological classes.

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SIS and SIR epidemic models under virtual dispersal

Cited by 2 publications

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Vector-borne diseases models with residence times – A Lagrangian perspective

Vector-borne diseases models with residence times – A Lagrangian perspective

From Bee Species Aggregation to Models of Disease Avoidance: The Ben-Hur effect

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