On Oscillatory Pattern of Malaria Dynamics in a Population with Temporary Immunity

Mugisha, Johnny; Luboobi, Livingstone S.

doi:10.1080/17486700701529002

Cited by 18 publications

(13 citation statements)

References 23 publications

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“…The parameter i a depends on the host age group in each patch. We also assume that the recovery rate i γ does not depend on age [5] but on how quickly the host receives treatment and history of their malaria infection. For patches…”

Section: A Himentioning

confidence: 99%

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Formulation of a Vector SIS Malaria Model in a Patchy Environment with Two Age Classes

Wairimu¹,

Sallet²,

Ogana³

2014

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 . Using Vidyasagar theorem [1], the graph of the reduced system is shown to be strongly connected and the system is a monotone dynamical system. This means that circulation of malaria parasites among the species and among the patches is strongly connected, hence transmission is sustained. We show that for the n-dimensional age structured system the positive orthant is positively invariant for all positive values of the variables.

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Section: A Himentioning

confidence: 99%

“…They are not bitten in same way as adults, [3] [4]. Most deaths occur in infants and parasitemia levels of infected individuals decrease with age [5]. The large areas affected by malaria make the spraying of every house impossible, [6].…”

Section: Introductionmentioning

confidence: 99%

Formulation of a Vector SIS Malaria Model in a Patchy Environment with Two Age Classes

Wairimu¹,

Sallet²,

Ogana³

2014

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“…The new variables, W and G, denote WTs and transgenics, as do the subscripts, w and g. Thus, F (W, G, t), the larval survival function, is given by Equations (4) with W + G replacing M. Equations (5) generalize the model (no transgenics, constant numbers of mosquitoes) studied by Tumüne et al [97]; for alternative approaches, see [55,79].…”

Section: Competition Between Gm and Wild-type Mosquitoesmentioning

confidence: 99%

Controlling malaria: competition, seasonality and ‘slingshotting’ transgenic mosquitoes into natural populations

Schaffer

Bronnikova

2009

Journal of Biological Dynamics

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Forty years after the World Health Organization abandoned its eradication campaign, malaria remains a public health problem of the first magnitude with worldwide infection rates on the order of 300 million souls. The present paper reviews potential control strategies from the viewpoint of mathematical epidemiology. Following MacDonald and others, we argue in Section 1 that the use of imagicides, i.e., killing, or at least repelling, adult mosquitoes, is inherently the most effective way of combating the pandemic. In Section 2, we model competition between wild-type (WT) and plasmodium-resistant, genetically modified (GM) mosquitoes. Under the assumptions of inherent cost and prevalence-dependant benefit to transgenics, GM introduction can never eradicate malaria save by stochastic extinction of WTs. Moreover, alternative interventions that reduce prevalence have the undesirable consequence of reducing the likelihood of successful GM introduction. Section 3 considers the possibility of using seasonal fluctuations in mosquito abundance and disease prevalence to 'slingshot' GM mosquitoes into natural populations. By introducing GM mosquitoes when natural populations are about to expand, one can 'piggyback' on the yearly cycle. Importantly, this effect is only significant when transgene cost is small, in which case the non-trivial equilibrium is a focus (damped oscillations), and piggybacking is amplified by the system's inherent tendency to oscillate. By way of contrast, when transgene cost is large, the equilibrium is a node and no such amplification is obtained.

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“…As in Tumwiine et al (2007) [19], the term abS H I V /N H denotes the rate at which the human hosts S H get infected by infected mosquitoes I V and acS V I H /N H refers to the rate at which the susceptible mosquitoes S V are infected by the infected human hosts I H . In order to ensure that there is a nonzero flow of individuals into the protected class, we assume that π + ρΛ > 0.…”

Section: Formulation Of the Modelmentioning

confidence: 99%

“…The Chitnis et al (2006) [3] model excludes the direct infectious-to-susceptible recovery in humans that is considered in (Ngwa and Shu, 2000 [17]). In Tumwiine et al (2007) [19] a model based on susceptible-infectious-recovered-susceptible (SIRS) pattern for humans and susceptible-infectious (SI) pattern for mosquitoes was considered. It was es-tablished that recoveries and temporary immunity keep the populations at oscillation patterns and eventually converge to a steady state.…”

Section: Introductionmentioning

confidence: 99%

Threshold and Stability Results for a Malaria Model in a Population With Protective Intervention Among High‐risk Groups

Mugisha

Luboobi

2008

Mathematical Modelling and Analysis

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Abstract. We develop a mathematical model for the dynamics of malaria with a varying population for which new individuals are recruited through immigration and births. In the model, we assume that non-immune travellers move to endemic regions with sprays, smear themselves with jelly that is repellent to mosquitoes on arrival in malarious regions, others take long term antimalarials, and pregnant women and infants receive full treatment doses at intervals even when they are not sick from malaria (commonly referred to as intermittent preventive therapy). We introduce more features that describe the dynamics of the disease for the control strategies that protect the above vulnerable groups. The model analysis is done and equilibrium points are analyzed to establish their local and global stability. The threshold of the disease, the control reproduction number, is established for which the disease can be eliminated.

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On Oscillatory Pattern of Malaria Dynamics in a Population with Temporary Immunity

Cited by 18 publications

References 23 publications

Formulation of a Vector SIS Malaria Model in a Patchy Environment with Two Age Classes

Formulation of a Vector SIS Malaria Model in a Patchy Environment with Two Age Classes

Controlling malaria: competition, seasonality and ‘slingshotting’ transgenic mosquitoes into natural populations

Threshold and Stability Results for a Malaria Model in a Population With Protective Intervention Among High‐risk Groups

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