Global Analysis of an SEIR Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate

Ren, Xiaomei; Zhang, Tiansi

doi:10.4236/jamp.2017.512188

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Several mathematical models have been developed to study the dynamics of malaria spread. We can cite the models S h I h S h -S v I v S v of Ross, the models S h I h R h S h -S v I v in [2][3][4], and the models S h E h I h R h S h in [5,6]. The mathematical theory of the spread of malaria was solidified by Reiner et al [7] in the 1960s.…”

Section: Introductionmentioning

confidence: 99%

On a Stochastic Approach to Extensions of the Susceptible‐Infected‐Susceptible (SIS) Model Applied to Malaria

Drabo,

Bere,

Nitiema

2024

Journal of Applied Mathematics

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This work presents a stochastic model of malaria spread. We first calculated the basic reproduction number R0 of the models ShIhRhSh‐SvIv and ShLhIhRhSh‐SvLvIv in order to show that the malaria-free equilibrium is asymptotically stable; then, we used a finite Markov chain model to describe the interactions between the different compartments of the model SeLeIeReSe‐SaLaIaRaSa‐SvIv. We carried out numerical simulations of our results for two types of transmission zones: a zone with low malaria transmission and an endemic zone. Through these simulations, we first determined the invariant stationary distribution π∗ of the model, and then, we found that the use of the indoor residual spraying (IRS) method by regular application of insecticides is more effective for the elimination of malaria than the use of long-acting impregnated mosquito nets (LLINs).

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Section: Introductionmentioning

confidence: 99%

On a Stochastic Approach to Extensions of the Susceptible‐Infected‐Susceptible (SIS) Model Applied to Malaria

Drabo,

Bere,

Nitiema

2024

Journal of Applied Mathematics

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“…Thus, a minimum value of means that educated individuals would not be able to spread the disease, and a maximum value of means that both types of infectives transmit the disease with the same rate. Along these lines, a type of infection force has been defined as (Ren and Zhang 2017 ; Ponciano and Capistran 2011 ).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate

2021

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In this article, we study the dynamics of a new proposed age-structured population mathematical model driven by a seasonal forcing function that takes into account the variability of the climate. We introduce a generalized force of infection function to study different potential disease outcomes. Using nonlinear analysis tools and differential inequalities theorems, we obtain sufficient conditions that guarantee the existence of a positive periodic solution. Moreover, we provide sufficient conditions that assure the global attractivity of the positive periodic solution. Numerical results corroborate the theoretical results in the sense that the solutions are positive and the periodic solution is a global attractor. This type of models are important, since they take into account the variability of the weather and the impact on some epidemics such as the current COVID-19 pandemic.

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Analysis of SEIR epidemic patch model with nonlinear incidence rate, vaccination and quarantine strategies

Zhu

2022

Mathematics and Computers in Simulation

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Global Analysis of an SEIR Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate

Abstract: In this paper, a SEIR model with ratio-dependent transmission rate in the

Cited by 3 publications

References 14 publications

On a Stochastic Approach to Extensions of the Susceptible‐Infected‐Susceptible (SIS) Model Applied to Malaria

On a Stochastic Approach to Extensions of the Susceptible‐Infected‐Susceptible (SIS) Model Applied to Malaria

Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate

Analysis of SEIR epidemic patch model with nonlinear incidence rate, vaccination and quarantine strategies

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