A mathematical model for the transmission of Plasmodium vivax malaria

Ishikawa, Hirofumi; Ishii, Akira; Nagai, Nobuhiko; Ohmae, Hiroshi; Harada, Masakazu; Suguri, Setsuo; Leafasia, Judson

doi:10.1016/s1383-5769(02)00084-3

Cited by 51 publications

(40 citation statements)

References 13 publications

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“…For P. vivax , however, MDA with drugs that treat only blood-stage infection are predicted to have only a transient effect, whilst addition of a liver-stage drug is predicted to be highly effective 49, 59, 60. This is due to the large effect at a population-level of relapsing infection [61].…”

Section: Expanding the Use Of Antimalarial Drugsmentioning

confidence: 99%

Mathematical Modelling to Guide Drug Development for Malaria Elimination

Slater

Okell

Ghani

2017

Trends in Parasitology

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Mathematical models of the dynamics of a drug within the host are now frequently used to guide drug development. These generally focus on assessing the efficacy and duration of response to guide patient therapy. Increasingly, antimalarial drugs are used at the population level, to clear infections, provide chemoprevention, and to reduce onward transmission of infection. However, there is less clarity on the extent to which different drug properties are important for these different uses. In addition, the emergence of drug resistance poses new threats to longer-term use and highlights the need for rational drug development. Here, we argue that integrating within-host pharmacokinetic and pharmacodynamic (PK/PD) models with mathematical models for the population-level transmission of malaria is key to guiding optimal drug design to aid malaria elimination.

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Section: Expanding the Use Of Antimalarial Drugsmentioning

confidence: 99%

Mathematical Modelling to Guide Drug Development for Malaria Elimination

Slater

Okell

Ghani

2017

Trends in Parasitology

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“…The proportion of infected bites on both human and mosquito that produces an infection is b = c = 0.5 Le Menach et al, 2005). The number of mosquitoes per human host could be various, we take m = 2 Ishikawa et al, 2003). The per capita mortality rate of mosquitoes μ varies from 0.05 to 0.5 per day Aron and May, 1982;Le Menach et al, 2005), here we take μ = 0.05 per day.…”

Section: Numerical Simulationsmentioning

confidence: 99%

On the Delayed Ross–Macdonald Model for Malaria Transmission

2008

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The feedback dynamics from mosquito to human and back to mosquito involve considerable time delays due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the human and the mosquito, we first propose a delayed RossMacdonald model. Then we calculate the basic reproduction number R 0 and carry out some sensitivity analysis of R 0 on the incubation periods, that is, to study the effect of time delays on the basic reproduction number. It is shown that the basic reproduction number is a decreasing function of both time delays. Thus, prolonging the incubation periods in either humans or mosquitos (via medicine or control measures) could reduce the prevalence of infection.

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“…Value Reference a, the average daily biting rate on man by a single mosquito 0.29/day [14,18] b, the proportion of bites on man that produce an infection 0.75 [18] c, the probability that a mosquito becomes infectious 0.75 [18] g, the per capita rate of loss of immunity in human hosts 0.000017/day [14] r, the rate at which human hosts acquire immunity 0.00019/day [5] d, the per capita death rate due to the disease 0.333 [25] n, the rate of recovery of human hosts from the disease 0.0022/day [3,8] l h , the per capita natural birth rate of humans 0.0015875/day [8] l v , the per capita natural birth rate of the mosquitoes 0.071/day [8] m h , the per capita natural death rate of the humans 0.00004/day [5] m v , the per capita natural death rate of the mosquitoes 0.05/day [19] On malaria dynamics is need for effective drugs, treated bed nets and insecticides that would reduce the mosquito population. Since malaria induced immunity is not everlasting, it remains a major obstacle to eradicate the disease even if individuals are protected.…”

Section: Parametermentioning

confidence: 99%

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

Mugisha

Luboobi

2007

Computational and Mathematical Methods in Medicine

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We use a model to study the dynamics of malaria in the human and mosquito population to explain the stability patterns of malaria. The model results show that the disease-free equilibrium is globally asymptotically stable and occurs whenever the basic reproduction number, R 0 is less than unity. We also note that when R 0 . 1, the disease-free equilibrium is unstable and the endemic equilibrium is stable. Numerical simulations show that recoveries and temporary immunity keep the populations at oscillation patterns and eventually converge to a steady state.

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A mathematical model for the transmission of Plasmodium vivax malaria

Cited by 51 publications

References 13 publications

Mathematical Modelling to Guide Drug Development for Malaria Elimination

Mathematical Modelling to Guide Drug Development for Malaria Elimination

On the Delayed Ross–Macdonald Model for Malaria Transmission

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

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