Epidemiological models with age structure, proportionate mixing, and cross-immunity

Castillo‐Chavez, Carlos; Hethcote, Herbert W.; Andreasen, Viggo; Levin, Simon A.; Liu, W. M.

doi:10.1007/bf00275810

Cited by 285 publications

(212 citation statements)

References 24 publications

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“…Also, cross-immunity factors are bounded between zero and one, since they decrease susceptibility. Detailed studies of these systems can be found in Castillo-Chavez et al (1989), Andreasen et al (1997), Dawes and Gog (2002), and Abu- Raddad and Ferguson (2005). While the steady states and reduced system analysis for the general cross-immunity model are similar to the ADE model, the ADE model exhibits interesting oscillatory and desynchronization behavior that is not found in cross-immunity model.…”

Section: Description Of General N-serotype Modelmentioning

confidence: 93%

Instabilities in multiserotype disease models with antibody-dependent enhancement

Billings

Schwartz

Shaw

et al. 2007

Journal of Theoretical Biology

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Section: Description Of General N-serotype Modelmentioning

confidence: 93%

Instabilities in multiserotype disease models with antibody-dependent enhancement

Billings

Schwartz

Shaw

et al. 2007

Journal of Theoretical Biology

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“…We decided to model this process through the use of a susceptibility coefficient similarly to the one used by (13] and (4]. This coefficient allows us to explore varying degrees of susceptibility to secondary infections and their effect on the asymptotic dynamics of the disease.…”

Section: Superinfection and Coexistencementioning

confidence: 99%

Competitive exclusion in a vector-host model for the dengue fever

Feng

Hernández²

1997

Journal of Mathematical Biology

311

189

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In this work we study a system of differential equations that models the population dynamics of an SIR vector transmitted disease with two pathogen strains. This model arose from our study of the population dynamics of dengue fever. The dengue virus presents four serotypes each of which induces host immunity but only certain degree of crossimmunity to the other different serotypes. The model studied here has been constructed as a paradigm for the study of the epidemiological trends in the disease and for the theoretical study of conditions that permit coexistence in competing strains. Dengue is mainly an epidemic disease in the Americas and this model is geared to generalize this type of dynamics. In the model two different strains of virus are considered with temporary cross-immunity. The model shows the existence of an unstable endemic state ('saddle' point). The nature of this equilibrium produces a transient behavior characterized as a quasi-steady state of long duration during which both dengue serotypes co-circulate. Conditions for asymptotic stability of the equilibria are discussed together with numerical simulations. We argue that the existence of competitive exclusion in this system is due to the interplay between the host superinfection process and the frequency-dependent (vector to host) contact rates.

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“…Second, it is not necessarily the case that these patterns can be easily expressed in tractable mathematics. Refined models based on typical social patterns such as partnership formation and dissolution [22,23], sexual network formations [24], or concurrent partnership [25] have been analyzed by various authors (see also [26,27,28]), and more recently in the context of HIV/AIDS transmission [29,30]. However such models are susceptible to unreliable data since sexual intercourses are difficult to track through statistical surveys or marital status.…”

Section: Discussionmentioning

confidence: 99%

Renaissance model of an epidemic with quarantine

Dobay

Gall

Rankin

et al. 2013

Journal of Theoretical Biology

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Quarantine is one possible solution to limit the propagation of an emerging infectious disease. Typically, infected individuals are removed from the population by avoiding physical contact with healthy individuals. A key factor for the success of a quarantine strategy is the carrying capacity of the facility. This is often a known parameter, while other parameters such as those defining the population structure are more difficult to assess. Here we develop a model where we explicitly introduce the carrying capacity of the quarantine facility into a susceptible-infected-recovered (SIR) framework. We show how the model can address the propagation and control of contact and sexually transmitted infections. We illustrate this by a case study of the city of Zurich during the 16th century, when it had to face an epidemic of syphilis. After Swiss mercenaries came back from a war in Naples in 1495, the authorities of the city addressed subsequent epidemics by, among others, placing infected members of the population in quarantine. Our results suggest that a modestly sized quarantine facility can successfully prevent or reduce an epidemic. However, false detection can present a real impediment for this solution. Indiscriminate quarantine of individuals can lead to the overfilling of the facility, and prevent the intake of infected individuals. This results in the failure of the quarantine policy. Hence, improving the rate of true over false detection becomes the key factor for quarantine strategies. Moreover, in the case of sexually transmitted infections, asymmetries in the male to female ratio, and the force of infection pertaining to each sex and class of sexual encounter can alter the effectiveness of quarantine measures. For example, a heterosexually transmitted disease that mainly affects one sex is harder to control in a population with more individuals of the opposite sex. Hence an imbalance in the sex ratios as seen in situations such as mining colonies, or populations at war, can present impediments for the success of quarantine policies. AbstractQuarantine is one possible solution to limit the propagation of an emerging infectious disease. Typically, infected individuals are removed from the population by avoiding physical contact with healthy individuals. A key factor for the success of a quarantine strategy is the carrying capacity of the facility. This is often a known parameter, while other parameters such as those defining the population structure are more difficult to assess. Here we develop a model where we explicitly introduce the carrying capacity of the quarantine facility into a susceptible-infected-recovered (SIR) framework. We show how the model can address the propagation and control of contact and sexually transmitted infections. We illustrate this by a case study of the city of Zurich during the 16 th century, when it had to face an epidemic of syphilis. After Swiss mercenaries came back from a war in Naples in 1495, the authorities of the city addressed subsequent epidemics by, amon...

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Epidemiological models with age structure, proportionate mixing, and cross-immunity

Cited by 285 publications

References 24 publications

Instabilities in multiserotype disease models with antibody-dependent enhancement

Instabilities in multiserotype disease models with antibody-dependent enhancement

Competitive exclusion in a vector-host model for the dengue fever

Renaissance model of an epidemic with quarantine

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