Global Analysis of New Malaria Intrahost Models with a Competitive Exclusion Principle

Iggidr, Abderrahman; Kamgang, Jean Claude; Sallet, Gauthier; Tewa, Jean Jules

doi:10.1137/050643271

Cited by 73 publications

(77 citation statements)

References 58 publications

(86 reference statements)

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“…The frequency for a single variant is ap . For the case when the AP solution corresponds (16), is larger than that for (b) AP oscillations, Equation (15). Asymptotic approximations of (b) AP oscillations, Equations (18), are shown as the dashed curves and fit well with numerical solutions to Equations (7), shown as the solid curves.…”

Section: Linear Stabilitymentioning

confidence: 93%

“…The non-positive equilibria have some of the Y j = 0 and allow one to analyse the competitive exclusion principle by representing extinction of one or more of the variants [1,4,7,8,15]. We are not interested in the competition between steady states but, rather, the competition between either synchronous or asynchronous oscillations.…”

Section: Scaled Model With Global Couplingmentioning

confidence: 99%

See 1 more Smart Citation

Synchronous versus asynchronous oscillations for antigenically varyingPlasmodium falciparumwith host immune response

Mitchell

Carr

2012

Journal of Biological Dynamics

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We consider a deterministic intra-host model for Plasmodium falciparum (Pf ) malaria infection, which accounts for antigenic variation between n clonal variants of PfEMP1 and the corresponding host immune response (IR). Specifically, the model separates the IR into two components, specific and cross-reactive, respectively, in order to demonstrate that the latter can be a mechanism for the sequential appearance of variants observed in actual Pf infections. We show that a strong variant-specific IR relative to the crossreactive IR favours the asynchronous oscillations (sequential dominance) over the synchronous oscillations in a number of ways. The decay rate of asynchronous oscillations is smaller than that for the synchronous oscillations, allowing for the parasite to survive longer. With the introduction of a delay in the stimulation of the IR, we show that only a small delay is necessary to cause persistent asynchronous oscillations and that a strong variant-specific IR increases the amplitude of the asynchronous oscillations.

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Section: Linear Stabilitymentioning

confidence: 93%

Section: Scaled Model With Global Couplingmentioning

confidence: 99%

Synchronous versus asynchronous oscillations for antigenically varyingPlasmodium falciparumwith host immune response

Mitchell

Carr

2012

Journal of Biological Dynamics

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“…The global stability of SP model, eventually with latent classes, with mass action is proved in [15,32]. Stability of intra-host models with different strains [30] (which contained as a particular case, SE 1 · · · E k IR models with multiple strains) is treated in [1,30]. The stability of differential and staged progression latent classes, with one infectious class is solved in [32].…”

Section: Introductionmentioning

confidence: 99%

Epidemiological Models and Lyapunov Functions

Fall

Iggidr

Sallet

et al. 2007

Math. Model. Nat. Phenom.

187

210

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Abstract. We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential infectivity and staged progression models. In the two cases we prove that if the basic reproduction ratio R 0 ≤ 1, then the disease free equilibrium is globally asymptotically stable. If R 0 > 1, there exists an unique endemic equilibrium which is asymptotically stable on the positive orthant.

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“…To this end, we use the same Lyapunov functions as those used in [55,[58][59][60][61][62] to demonstrate the global stability of the endemic equilibrium of SEIR, SEIS, and SIR models.…”

Section: Appendix: Global Stability Of the Endemic Equilibrium Of Modmentioning

confidence: 99%

Modeling and analysis of the transmission dynamics of tuberculosis without and with seasonality

Bowong

Kurths

2011

Nonlinear Dyn

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A deterministic model of tuberculosis without and with seasonality is designed and analyzed into its transmission dynamics. We first present and analyze a tuberculosis model without seasonality, which incorporates the essential biological and epidemiological features of the disease. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with one or more stable endemic equilibria when the associated basic reproduction number is less than unity. The statistical data of tuberculosis (TB) cases show seasonal fluctuations in many countries. Then, the extension of our TB model by incorporating seasonality is developed and the basic reproduction ratio is defined. Parameter values of the model are estimated according to demographic and epidemiological data in Cameroon. The simulation results are in good accordance with the seasonal variation of the reported cases of active TB in Cameroon.

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Global Analysis of New Malaria Intrahost Models with a Competitive Exclusion Principle

Cited by 73 publications

References 58 publications

Synchronous versus asynchronous oscillations for antigenically varyingPlasmodium falciparumwith host immune response

Synchronous versus asynchronous oscillations for antigenically varyingPlasmodium falciparumwith host immune response

Epidemiological Models and Lyapunov Functions

Modeling and analysis of the transmission dynamics of tuberculosis without and with seasonality

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