Mathematical analysis of an age-structured model for malaria transmission dynamics

Forouzannia, Farinaz; Gumel, Abba B.

doi:10.1016/j.mbs.2013.10.011

Cited by 56 publications

(46 citation statements)

References 35 publications

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“…In the work by Kamangira [44], modeled immune response and or drug intervention at the asexual blood stage of Plasmodium falciparum. Other scholars like Tumwiine and Forouzannia [24,65] studied age compartmental models and used the system of age-structured partial equations integrated over age to a system of delay differential equations. While Nannyonga [52] considered the severe case of malaria and the results showed that malaria parasites can be absorbed in already infected red blood cells, causing faster rapture of cells and can lead anenia.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modelling of the in-host dynamics of malaria and the effects of treatment

Tabo¹,

Luboobi²,

Ssebuliba³

2017

J. Math. Computer Sci.

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Malaria research and mathematical models have mainly concentrated on malaria Plasmodium at the blood stage. This has left many questions concerning models of parasite dynamics in the liver and within the mosquito. These concerns are anticipated to keep scientists busy trying to understand the biology of the parasite for some more years to come. Thorough knowledge of parasite biology helps in designing appropriate drugs targeting particular stages of Plasmodium. To achieve this, there is need to study the transmission dynamics of malaria and the interaction between the infection in the liver, blood and mosquito using a mathematical model. In this study, a within-host mathematical model is proposed and considers the dynamics of P. falciparum malaria from the liver to the blood in the human host and then to the mosquito. Several techniques, including center manifold theory and sensitivity analysis are used to understand relevant features of the model dynamics like basic reproduction number, local and global stability of the disease-free equilibrium and conditions for existence of the endemic equilibrium. Results indicate that the infection rate of merozoites, the rate of sexual reproduction in gametocytes, burst size of both hepatocytes and erythrocytes are more sensitive parameters for the onset of the disease. However, a treatment strategy using highly effective drugs against such parameters can reduce on malaria progression and control the disease. Numerical simulations show that drugs with an efficacy above 90% boost healthy cells, reduce infected cells and clear parasites in human host. Therefore more needs to be done such as research in parasite biology and using highly effective drugs for treatment of malaria.

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Section: Introductionmentioning

confidence: 99%

Mathematical modelling of the in-host dynamics of malaria and the effects of treatment

Tabo¹,

Luboobi²,

Ssebuliba³

2017

J. Math. Computer Sci.

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“…Moreover, in endemic regions, children under 5, pregnant women and non-immune adults are most at risk of malaria mortality [12]. Indeed, there are currently over 100 countries where there is a risk of malaria transmission, and these are visited by more than 125 million international travellers every year.…”

Section: Introductionmentioning

confidence: 99%

A mathematical model of malaria transmission in a periodic environment

Traoré

Sangaré

Traoré

2018

Journal of Biological Dynamics

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In this paper, we present a mathematical model of malaria transmission dynamics with age structure for the vector population and a periodic biting rate of female anopheles mosquitoes. The human population is divided into two major categories: the most vulnerable called non-immune and the least vulnerable called semi-immune. By applying the theory of uniform persistence and the Floquet theory with comparison principle, we analyse the stability of the diseasefree equilibrium and the behaviour of the model when the basic reproduction ratio R 0 is greater than one or less than one. At last, numerical simulations are carried out to illustrate our mathematical results. ARTICLE HISTORY

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“…Since Kermack and Mckendric [7] introduced the SIR model to understand the dynamic of epidemic system, many mathematical models have been proposed since then with the intention to understand the qualitative behaviour for various disease like dengue [15,16,18], malaria [11,12], West Nile virus [13,14], Influenza [6,19], swine flu [17], etc. Many mathematical model have been developed to understand the spread of influenza and explored strategies for control the spread [6,19,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

Assessing the Potential of Medical-Mask and Drug-Treatment in Controlling Influenza Disease

Rohmah¹,

Handari²,

Aldila³

2017

Int. J. of Pure and Appl. Math.

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Abstract:A classical SIS model for influenza disease with two intervention strategies such as medical mask and drug treatment from deterministic framework was extended in this paper into a stochastic differential equation (SDE). The SDE model was constructed by introducing a random perturbation in successful contact rate parameter. The concern of this study is focused in to two aspects based on from mathematical and epidemiological point of view. From mathematical point of view, the basic reproduction number from deterministic framework (known as R0) was analyzed and compared with the stochastic threshold parameter (we call it as ρ0). As well as R0 in deterministic model, the ρ0 also linked into the extinction and persistence condition of endemic equilibrium. If ρ0 < 1, then the SDE system will reach the extinction of influenza disease with probability one. Otherwise, if ρ0 > 1 then influenza disease will persist. However, we found a situation where ρ0 gives a contrast result compared to R0 as a consequence of random perturbation in successful contact rate parameter. From epidemiological point of view, we found that medical mask and drug treatment intervention and successful contact rate influence the dynamic of influenza spread in our model, which cangive us a direction about the best strategy to regulate influenza spreads. Some numerical simulations were generated to support the analytical results.

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Mathematical analysis of an age-structured model for malaria transmission dynamics

Cited by 56 publications

References 35 publications

Mathematical modelling of the in-host dynamics of malaria and the effects of treatment

Mathematical modelling of the in-host dynamics of malaria and the effects of treatment

A mathematical model of malaria transmission in a periodic environment

Assessing the Potential of Medical-Mask and Drug-Treatment in Controlling Influenza Disease

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