Modelling the ability of mass drug administration to interrupt soil-transmitted helminth transmission: Community-based deworming in Kenya as a case study

The World Health Organization has recommended the application of mass drug administration (MDA) in treating high prevalence neglected tropical diseases such as soil-transmitted helminths (STHs), schistosomiasis, lymphatic filariasis, onchocerciasis and trachoma. MDA—which is safe, effective and inexpensive—has been widely applied to eliminate or interrupt the transmission of STHs in particular and has been offered to people in endemic regions without requiring individual diagnosis. We propose two mathematical models to investigate the impact of MDA on the mean number of worms in both treated and untreated human subpopulations. By varying the efficay of drugs, initial conditions of the models, coverage and frequency of MDA (both annual and biannual), we examine the dynamic behaviour of both models and the possibility of interruption of transmission. Both models predict that the interruption of transmission is possible if the drug efficacy is sufficiently high, but STH infection remains endemic if the drug efficacy is sufficiently low. In between these two critical values, the two models produce different predictions. By applying an additional round of biannual and annual MDA, we find that interruption of transmission is likely to happen in both cases with lower drug efficacy. In order to interrupt the transmission of STH or eliminate the infection efficiently and effectively, it is crucial to identify the appropriate efficacy of drug, coverage, frequency, timing and number of rounds of MDA.


Comment (8):
Abstract. Responsive to 'preventive chemotherapy'. Is the mean number of worms the best way of perceiving the effort to reduce STH to "no longer of public health significant" (< 10% prevalence of any STH and < 1% moderate/heavy infections) Do you actually mean worms of eggs per gram of faces? There is such enormous variance in the morbidity of epg by species that you cannot compare 100epg for hookworm with 100epg for Ascaris: the morbidity is grossly different.
Response: No, the mean number of worms in this article does not refer to worms of eggs per gram of faeces. The mean number of worms (M ) in this article refers to the average number of worms in a human population of density N at time t. We have made our definition explicit. (Page 4, lines 115-116, in red, as the other reviewer also raised this point.) Comment (9): L 12: I suggest 'preventive chemotherapy (PC)' is more appropriate than 'deworming' as one doesn't know if the individual has actually been de-wormed the worm burden will have reduced but whether it gets to zero will depend upon mostly the worm burden before treatment as well as the type of medicine used (more v less effective).
Response: Thank you very much for the suggestion and we have changed the "deworming" to "preventive chemotherapy" throughout. (Page 2, line 9 etc.) Comment (10): L 18: I don't think 'only' is helpful here as targeted chemo and selective chemo and mass chemo often coexist in a community. Response: We would like to apologize for unable to make any comment regarding this question as we do not have any data/information about this question. However, we provide some information; please refer to Comment (7).

Comment (14)
: L 26: PC should have been introduced earlier and then the abbreviation can be used throughout the manuscript.
Response: Thanks. We have fixed it throughout this manuscript.
Comment (15): L 30: I would add that the strategy needs to be respectful of the local context, traditional authorities, customs and belief systems if the last mile toward STH control is to be effective and that control to be maintained. I suggest that STH recrudesce is almost inevitable if these are not taken into consideration: if personal and environment hygiene are not considered.
resurgence. Rebound STH infection after mass MDA and apparent 'control' has been well documented for over 30 years. Response: This raises a good point. Eigenvalues are used to determine stability of equilibria for multidimensional systems. However, since our system is onedimensional, the eigenvalue is equivalent to the derivative. We have thus streamlined our argument and added an explanation of why we are interested in stability of equilibria. This has simplified the complexity and hopefully not alienated readers for whom linear algebra may be a distant memory! (Page 5, lines 140-147 and Page 6, 154-155) Comment (4): L 177 "To find the endpoints of an impulsive orbit..." What is an impulsive orbit? Why do we need to calculate them? Response: Yes, some of the real parameter values are difficult to obtain, such as the clumping parameter (k), R 0 and initial values especially in specific region, etc. In these cases, we choose arbitrary parameter values that fulfill certain conditions if there are any (for example, the conditions as stated in the claim of Comment (3)).
Comment (6): How is the drug efficacy interpreted? Is it assuming perfect adherence? Is it the clearance rate? Response: All models in this paper are new except models (1) and (2). Models (1) and (2), proposed by Anderson and May [1], are our inspiration for the study, but we develop other models, such as (3)-(4)  The application to Kenya data is underwhelming. The prevalence is averaged over the whole country, making the application very broad. It is not shown methodically that only (b) and (c) strategies are considered in this paper. There is a lack of clarity with regards to how many MDA rounds are used in (b) compared to (c). Results are converted from decimals to percentages in an inconsistent manner. The plots are provided without explanation as to the meaning ofM etc (plots should be intepretable without having to read the paper).
Response: We have been guided by the impact of TUMIKIA community-based biannual and annual deworming strategies. We have added the number of rounds of MDA (Page 15, lines 323-324), converted all results to decimal points and fixed all the plots. (Figures 2-12) We thank the reviewer for flagging these.

Comment (9):
Abstract -Don't include parameter notation in the abstract.
-The acronym STH is introduced early on, and then throughout the paper the authors switch from writing out soil-transmitted helminthiasis in full, and using STH.

Reviewer # 3
This reviewer notes that "The problem that this manuscript takes in consideration is of great importance in some regions of the world. The authors carry on their analises with the help of some Mathematical models described by ODEs systems. Of special interest is the carefulness that the author put in the derivation of the form of constitutive functions. The numerical results are carefully compared with real data. The author discuss about some possible restrictions on the applicability of their study.The paper is clear and well organized, in my opinion it can be published in the present form." There is no change to be made.
In summary, we feel that these revisions have addressed all the points raised by the reviewers and hope that the manuscript is now acceptable.