The Dynamics of Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission

Naji, Raid Kamel; Hussien, Reem Mudar

doi:10.1155/2016/4907964

Cited by 30 publications

(26 citation statements)

References 22 publications

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“…Using Sotomayor's Theorem [16] we prove the analytical conditions required for a transcritical bifurcation between E 2 and E 3 to occur. Also, using well known conditions (see, for example [8,17]) we have shown that a Hopf bifurcation occcurs in E 3 at the threshold value µ * , giving rise to sustained population oscillations [14,15,20]. Point E 2 cannot give rise to oscillations, since both eigenvalues are always real.…”

Section: Bifurcationsmentioning

confidence: 57%

A Mathematical Model to describe the herd behaviour considering group defense

Assis¹,

Pazim

Malavazi

et al. 2020

Applied Mathematics and Nonlinear Sciences

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A model for predator-prey interactions with herd behaviour is proposed. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). The model is analysed using standard stability and bifurcations techniques. We prove that the system undergoes a Hopf bifurcation as we vary the parameter that represents the efficiency of predators (dependent on the predation rate, for instance), giving rise to sustained oscillations in the system. The proposed model appears to possess more realistic features than the previous approaches while being also relatively easier to analyse and understand.

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Section: Bifurcationsmentioning

confidence: 57%

A Mathematical Model to describe the herd behaviour considering group defense

Assis¹,

Pazim

Malavazi

et al. 2020

Applied Mathematics and Nonlinear Sciences

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“…To study the local bifurcations near the equilibrium points of Model , we use Sotomayor's theorem. ()…”

Section: Bifurcationsmentioning

confidence: 99%

“…Proof For systems in four‐dimensional spaces, for a Hopf bifurcation to occur, the following conditions should be satisfied(): The characteristic equation at E 2 has two real and negative eigenvalues and two complex eigenvalues; τ 1 ( m ∗ )=0; the transversality condition

false(\frac{d}{d m} τ_{1} false(m false) false) |_{m = m^{*}}

. □…”

Section: Bifurcationsmentioning

confidence: 99%

A mathematical model for bovine tuberculosis among buffaloes and lions in the Kruger National Park

Assis

Massad

Assis

et al. 2017

Math Methods in App Sciences

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In this paper, a model for the spread of tuberculosis between buffaloes and lions is presented and analyzed. The most important system parameters are identified: vertical and horizontal disease transmission among the buffaloes and the influence of intraspecific competition between healthy and diseased buffaloes on the infected buffaloes population. Removal of diseased prey appears to be the most effective strategy to render the ecosystem disease free.

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“…To make a study about the local bifurcations near the equilibrium points of model (4.2), we use the Sotomayor theorem [70,67].…”

Section: Bifurcationsmentioning

confidence: 99%

“…Proof. For systems in four-dimensional spaces, for a Hopf bifurcation to occur, the following conditions should be satisfied [30,89,67]:…”

Section: Hopf Bifurcationmentioning

confidence: 99%

Mathematical models for ecoepidemiological interactions, with applications to herd behaviour and bovine tuberculosis, and evolutionary interactions of alarm calls

Assis¹

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This thesis presents several nonlinear mathematical models applied to ecoepidemiology and evolution. A detailed study involving predator-prey type models considering an alternative resource for the predator was carried out, investigating the situation of infection in the prey and in the predator on separate models. Such study served as a theoretical contribution to the investigation of problems such as bovine tuberculosis in wild animal species presented in a specific model. We also developed models to explain the evolution of alarm calls in species of birds and mammals. The theoretical framework adopted for those evolution models is that of Population Ecology. The models were developed using Ordinary Differential Equations (ODEs) to describe the population dynamics. The biological assumptions of the systems that we wanted to analyse were enumerated and explained.

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The Dynamics of Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission

Cited by 30 publications

References 22 publications

A Mathematical Model to describe the herd behaviour considering group defense

A Mathematical Model to describe the herd behaviour considering group defense

A mathematical model for bovine tuberculosis among buffaloes and lions in the Kruger National Park

Mathematical models for ecoepidemiological interactions, with applications to herd behaviour and bovine tuberculosis, and evolutionary interactions of alarm calls

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