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. 2020 Jan 24;15(1):e0227919.
doi: 10.1371/journal.pone.0227919. eCollection 2020.

A Mathematical Model for Assessing the Effectiveness of Controlling Relapse in Plasmodium Vivax Malaria Endemic in the Republic of Korea

Free PMC article

A Mathematical Model for Assessing the Effectiveness of Controlling Relapse in Plasmodium Vivax Malaria Endemic in the Republic of Korea

Sungchan Kim et al. PLoS One. .
Free PMC article


Malaria has persisted as an endemic near the Demilitarized Zone in the Republic of Korea since the re-emergence of Plasmodium vivax malaria in 1993. The number of patients affected by malaria has increased recently despite many controls tools, one of the reasons behind which is the relapse of malaria via liver hypnozoites. Tafenoquine, a new drug approved by the United States Food and Drug Administration in 2018, is expected to reduce the rate of relapse of malaria hypnozoites and thereby decrease the prevalence of malaria among the population. In this work, we have developed a new transmission model for Plasmodium vivax that takes into account a more realistic intrinsic distribution from existing literature to quantify the current values of relapse parameters and to evaluate the effectiveness of the anti-relapse therapy. The model is especially suitable for estimating parameters near the Demilitarized Zone in Korea, in which the disease follows a distinguishable seasonality. Results were shown that radical cure could significantly reduce the prevalence level of malaria. However, eradication would still take a long time (over 10 years) even if the high-level treatment were to persist. In addition, considering that the vector's behavior is manipulated by the malaria parasite, relapse repression through vector control at the current level may result in a negative effect in containing the disease. We conclude that the use of effective drugs should be considered together with the increased level of the vector control to reduce malaria prevalence.

Conflict of interest statement

The authors have declared that no competing interests exist.


Fig 1
Fig 1. Normalized histogram of incubation periods between 2001 and 2010 (left), and time to first relapse (right) in Korea.
Fig 2
Fig 2. Schematic diagram of the model (1).
Human classes are represented as green rectangles with rounded corners, and mosquito classes as elongated blue hexagons. Arrows indicate the directions of transition between classes and dotted lines indicate the relationships between actions.
Fig 3
Fig 3. Approximating the empirical cumulative distribution function (ECDF) of IP to a 20-chained Coxian distribution (left), and that of TTFR to a 12-chained Coxian distribution (right).
Solid lines represent survival functions in each of the figures. Note that both fitted curves express multimodality.
Fig 4
Fig 4. Fitted model results.
The solid blue line indicates the model results representing weekly incidence with best fitted parameters and the dots are averaged over the data of weekly cases for each of the 4 weeks.
Fig 5
Fig 5. Seasonal reproduction number against time (left), and the percentage of the contribution of relapse in the seasonal reproduction number, R%, against κ (right).
In the left panel, the blue solid line records Rs in the absence of any control (κ = 0) and red dashed line records Rs in the presence of complete control (κ = 1).
Fig 6
Fig 6. Model result of the percentage of infectious humans with the current level of control.
The blue solid line shows the total number of infectious humans, Ip + Ir, the red dashed line indicates primary infected humans, Ip, and the yellow dotted line indicates infectious individuals who have relapsed, Ir.
Fig 7
Fig 7. Model results of Ip + Ir, Ip, and Ir with control.
Control starts at 2 and remains constant for 5 years with a rate κ.
Fig 8
Fig 8. The percentage of drops in yearly cases after control.
Fig 9
Fig 9. The effectiveness of relapse control considering manipulated behavior of mosquitoes.
Left colormap shows the percentages of reduction in yearly cases during 5-year control against κ and an increasing rate in the force of infection. A positive value indicates that the case is decreasing through control, and a negative value means the opposite. In the left panel, we assume that manipulation occurs one year after control starts. The black solid line shows the contour that the percentage of drops is 0. The upper and lower figures on right show the percentages of infectiousness when κ = 0.9 and when there is a 10%, 30% increase in the force of infection in humans with one year delay in manipulation after the beginning of control methods, respectively.

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Grant support

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP)(NRF-2017R1A5A1015722).