Referee 2's review (Roly Gosling):

Prospects for sustainable malaria control in areas of mesoendemic transmission in sub Saharan Africa

General overview -main paper

This paper describes a simple model of malaria that is based on:

Susceptibles becoming infected and having an attack of severe malaria (compared to hospitalised malaria in the data sets).

These cases recover to a different susceptible stage from where they can move to a less severe disease state when they become infected.

The model is affected by force of infection (incidence of malaria) and changes in transmission over age

There are some assumptions:

Force of infection varies with age

There is differential infectiousness between states I1 and I2 that is not based on length of time of infection but on theta- something inherent in the 2 states.

Data

The model is tested against 8 data sets of cases of admitted malaria.

Parameter estimations

This section is unclear. I understand from the text that age- prevalence admission rates were used to estimate the constants of length of infection for I1 and I2, alpha the reduction in immunity over time without reinfection, k the effect of increase in force of infection with age (the authors have to explain this), c which is not explained.

Equilibrium analysis

I do not understand this part of the paper. This needs revision and clarification. The authors need to explain what this is in clearer language.

What I understand is that R0 = the rate of change of transmission/(time taken in severe disease+ new susceptibles) but I am unsure that this is true. I ask the authors to elaborate and explain.

Results

Length of time in state I1 = 25 days- in the text they call this time "clinical malaria" do they mean hospitalized malaria or clinical malaria ie some of I2. Do the authors mean that the average length of infection is 25 days or the average length of disease is 25 days? The same goes with "mild infection"-does this includes asymptomatic.

Figure 1A shows us the proportion of cases of malaria (is this infection or disease?) that end up in hospital. The authors use the word "Clinical malaria" but do they mean hospitalized malaria or do they mean parasitaemia plus symptoms and are they comparing against parasite prevalence? In 1B and 1C they are comparing against R0 but I am unclear whether the selected calculation for R0 is valid.

Figure 2 the sensitivity analysis is only valid if you accept the assumption that theta is real. The authors need to convince the reader that this is true. The ending message I got from this paragraph is that the reason for more severe malaria at lower transmission is because it, severe malaria, is more transmissible. This is not the case- the reason that more severe malaria is present (as a proportion of malaria infections) at low transmission is that there is less immunity. In high transmission settings there will be more cases of severe malaria than in a low transmission setting because there is more malaria. The authors must try to get their message across in a different way.

Discussion

The first paragraph describes length of infection - in the text in the results a different number are used (25 and 118 days) and in the discussion 14 and 270 days.

The conclusion of the second paragraph is not backed by this model although probably true as this model is not looking at infection but at severe disease.

Bistability is used frequently in this paper yet only explained in the 3rd paragraph of the discussion. The term is not well explained yet is heavily stressed by the authors. By definition of the model I1 lasts less than I2 as I2 includes asymptomatic infection which is not recognized and treated. The authors need to explain what is relevant about this finding, what bistability means in a comprehensible language. Maybe considering that transmission changes would help the reader. If malaria control is put into practice, the endemicity changes (as can be seen across Africa at the moment) therefore concluding that one state of endemicity makes eradication possible and stable vs another is not representing the real world.

The authors further confuse the issue in the 4th paragraph, where they state that there should be early detection and treatment of infection but talk about disease.

Limitations are well represented

Final concluding paragraph relies on their definition of R0 which I think needs further clarifications.

Supplementary material

This contains much of the information needed in the main paper. My view is that the paper should be comprehensible enough to induce enough interest in the reader to go for the supplementary material. Therefore the figure and explanation of the model move to the main paper as well as the bit on Bistability and R0. The sensitivity analysis can stay as a supplement. I think figure 2 and 3 could be moved to the supplement as these interest the modellers who will want to see them.

Criticisms- suggested additions to improve the paper

Abstract- no objectives unclear results and conclusions needs rewriting
Introduction- No objectives- add objectives
Maybe add about bistability as the authors use this word a lot and it is not explained until the discussion

Needs schematic of model to include different parameters
Interchangeable terms of clinical malaria, severe malaria, uncomplicated malaria. I believe the authors are using hospitalised cases of malaria ie severe malaria = I1, all other infections (both symptomatic and asymptomatic are grouped together) = I2. This definitely needs clarification as in the text many different terms are used and confuses the reader.

Assumption that force of infection increases with age is based on what? Is this human behaviour risk?
What reasons do the authors base their assumption that there is difference in infectiousness between states I1 and I2, ie where does theta come from, what is the biological plausibility of this?
Parameter estimation- needs clarification - maybe the word "confronting" is wrong.
Equilibrium analysis- R0 needs clarification as this is a major part of the conclusions. The assumptions made need to be stated and evidence given.
Results - the format that the parameters are given is confusing- the parameters should be explained in text as well as symbols and the correct units given ie if the authors are going to use days in the text - give days in the table.
Figures- definition of the y axis needs to be clear- is this hospitalised/ parasitaemic?

Conclusion

The paper has no clear objective and thus cannot answer the objectives.

The basic model needs defining to make sense (ie what is I1 and what is I2).

Basic assumptions of the model need to be backed with evidence or biological plausibility.

Explanation of the results needs to be clearer for the reader to understand the relevance (bistability as an example).

Recommendation

The authors can revise this manuscript to make it easier for the non-modeller to comprehend by switching some of the material in the supplementary part to the main paper and vice versa. Most of my comments are pretty minor.

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N.B. These are the comments made by the referee when reviewing an earlier version of this paper. Prior to publication the manuscript has been revised in light of these comments and to address other editorial requirements.