Transmission model of endemic human malaria in a partially immune population

Chiyaka, Christinah; Garira, Winston; Dube, Simiso

doi:10.1016/j.mcm.2006.12.010

Cited by 55 publications

(26 citation statements)

References 26 publications

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“…For our model, we augment the basic SIR model to include preventative measures as seen previously by other researchers [3,4,5]. We include the effects of ITNs and IRS preventative measures based on the fact that both methods are recommended for the prevention of malaria by the WHO.…”

Section: Model Formationmentioning

confidence: 99%

“…In addition, the "Recovered" category is included as a way to deal with the issue of partial immunity after recovering from infection, a simplifying assumption of the model. Biological evidence exists for partial immunity of humans over long periods of exposure and treatment for malaria [4,5,7]. We allow for humans, after being treated for malaria, to have a partial immunity to the parasite for some time after treatment of the disease results in recovery.…”

Section: Model Formationmentioning

confidence: 99%

“…The ode45 function evaluates the differential equations using an explicit 4 th order Runge-Kutta method for solving ODEs. In these simulations, initial population sizes are chosen based on populations used in similar studies I product of human transmission probability (.5) and biting rate (.5), from [3] II product of recovery rate (.005) and modified recovery rate (8.04), from [3] III sum of treatment rate (.2) and recovery rate (.005), from [3] IV product of mosquito transmission probability (.83) and biting rate (.5), from [3] V division by 365 allows for the rate to have the correct units of days [4,3,5]. The initial conditions used are S h = 300, E h = 0, I h = 1, R h = 0, S m = 300, E m = 0, and I m = 0.…”

Section: Model Solutionmentioning

confidence: 99%

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Modeling the Effects of Malaria Preventative Measures

Griffin

2013

SIURO

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Malaria is a serious and sometimes fatal epidemic affecting nearly half of the world's population and is the 5th leading cause of death by infectious disease world-wide. There are currently two recommended methods for prevention and eradication of the disease: insecticide-treated mosquito nets (ITNs) and indoor residual spraying (IRS), but efficacies and compliance vary from region to region. In this project, we look at the effects of ITNs and IRS as methods for eradication of malaria. To compare these methods, we develop a differential equation model and apply the next generation matrix method to determine the basic reproductive number. The differential equation model builds on classical SIR epidemiological models, with added constraints for the two preventative measures. Analysis shows that the effects of ITNs and IRS can help eradicate the disease. We find that the effect of ITNs is significantly greater than the effect of IRS. We conclude that the combination of compliance and efficacy for ITNs needs to be at least 61% and that there is no such percentage for IRS alone that will eradicate the disease. At a minimum, in combination, compliance and efficacy for ITNs needs to be at least 60% and compliance and efficacy for IRS needs to be at least 60%.

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Section: Model Formationmentioning

confidence: 99%

Section: Model Formationmentioning

confidence: 99%

Section: Model Solutionmentioning

confidence: 99%

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Modeling the Effects of Malaria Preventative Measures

Griffin

2013

SIURO

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“…Fever, headaches and vomiting are amongst the typical sypmtoms of the disease. The infection is caused by a species of Plasmodium which is a parasite transmitted by an infected mosquito of the Anopheles type [6]. One type of parasite causes malaria infections which can cause death in some cases, while other 3 types of the parasite cause a mild infection [5], [15].…”

Section: Introductionmentioning

confidence: 99%

“…Several authors have made modeling studies on the dynamics of malaria infection on a deterministic level [1], [2], [3], [5], [6], [13], [16]. While most of the vast literature on the modeling studies of malaria are deterministic studies, several studies examine stochastic aspects of the disease as well [9], [10], [14].…”

Section: Introductionmentioning

confidence: 99%

Stochastic and random models of Malaria Disease with vertical transmission

Kesemen¹,

Merdan²,

Bekiryazici³

2017

ntmsci

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Malaria is an infectious disease which affects both humans and animals. In this study, the existing mathematical model of malaria disease with vertical transmission is analyzed in random enviroment. Random effect terms are added to the parameters of the deterministic model to form a system of random differential equations. Similarly, stochastic noise is added to the deterministic system to obtain a stochastic model. Finally, the results from the deterministic, random and stochastic model are compared to comment on the random behavior of the disease.

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The Dynamical Behaviours of Diseases in Africa

Garira

2012

Handbook of Systems and Complexity in Health

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Transmission model of endemic human malaria in a partially immune population

Cited by 55 publications

References 26 publications

Modeling the Effects of Malaria Preventative Measures

Modeling the Effects of Malaria Preventative Measures

Stochastic and random models of Malaria Disease with vertical transmission

The Dynamical Behaviours of Diseases in Africa

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