Dynamical behavior of an epidemiological model with a demographic Allee effect

Usaini, Salisu; Lloyd, Alun L.; Anguelov, Roumen; Garba, Salisu M.

doi:10.1016/j.matcom.2016.04.010

Cited by 7 publications

(2 citation statements)

References 29 publications

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“…Moreover, kidnapping has various definitions in the literature with varying degree and success [6]. It is one of such ideas/behaviours that can correctly be described as a social epidemic which spread across vulnerable humans over time, for more examples (see [8,12,21,29,30,31,32]). Several types of kidnapping are commonly seen in the world.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modelling and analysis of Kidnapping dynamics

Usaini,

Rabiu,

Shitu Hassan

2024

IJAMR

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The problem of kidnapping as a social menace to a society is increasing in some African countries such as Nigeria. We therefore proposed a new deterministic mathematical model for the dynamics of Kidnapping in a community. This menace is considered like a two strains communicable disease with kidnapping propagation mission by kidnappers as one strain and adoption mission for kidnapped victims as the other strain to assess the impact of super-infection. The model exhibits four equilibrium points each of which is unique and asymptotically stable both locally and globally under certain conditions. We obtain the kidnapping propagation number where is the propagation number associated with strain . Another important threshold parameters associated with respective strains 1 and 2 are and . Indeed, we show that at most one strain invades the population if one of these parameters is less than unity. while the two strains coexist at endemic state when both and are greater than unity. The global stability results of the model equilibria are established by numerical simulations. This simulations results indicate that the super-infection destabilizes the coexistence equilibrium.

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Section: Introductionmentioning

confidence: 99%

Mathematical modelling and analysis of Kidnapping dynamics

Usaini,

Rabiu,

Shitu Hassan

2024

IJAMR

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“…There are some publications that analyze how feedback affects the diseases [6], [8], analyzed SIR-type models with negative feedback effects , and [3], [7] analyze Allee effect in populations in epidemiological systems. Both analyze their models with ordinary differential equations with a linear incidence rate with respect to the positive feedback effect.…”

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confidence: 99%

Implications of the delayed feedback effect on the stability of a SIR epidemic model

Cruz¹

2023

Sel.mat

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A basic mathematical model in epidemiology is the SIR (Susceptible–Infected–Removed) model, which is commonly used to characterize and study the dynamics of the spread of some infectious diseases. In humans, the time scale of a disease can be short and not necessarily fatal, but in some animals (for example, insects) this same short time scale can make the disease fatal if we take into account their life expectancy. In this work, we will see how a positive feedback effect (decrease of the susceptible population at small densities) in a SIR model can cause a qualitative characterization of the dynamics defined by the original SIR model. Finally, we will also show with numerical simulations how a delay in the feedback effect causes very interesting qualitative changes of the system with epidemiological significance.

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