Mitigating the externality of diseases of poverty through health aid

Externality exists in healthcare when an individual benefits from others being healthy as it reduces the probability of getting sick from illness. Healthy workers are considered to be the more productive labourers leading to a country’s positive economic growth over time. Several research studies have modelled disease transmission and its economic impact on a single country in isolation. We developed a two-country disease-economy model that explores disease transmission and cross-border infection of disease for its impacts. The model includes aspects of a worsening and rapid transmission of disease juxtaposed by positive impacts to the economy from tourism. We found that high friction affects the gross domestic product (GDP) of the lower-income country more than the higher-income country. Health aid from one country to another can substantially help grow the GDP of both countries due to the positive externality of disease reduction. Disease has less impact to both economies if the relative cost of treatment over an alternative (e.g. vaccination) is lower than the baseline value. Providing medical supplies to another country, adopting moderate friction between the countries, and finding treatments with lower costs result in the best scenario to preserve the GDP of both countries.

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RSOS-210732
This paper models the interaction between two countries through tourism mobility. An infectious disease with SIR dynamics is prevalent in each country, and the economic structure is modeled through a Solow growth model so that the savings rate is constant. Modeling the role of interaction between two countries taking into account disease prevalence as well as economic activity in understanding pandemics is important.
However, there are some issues in modeling choices that affect what one can learn from the paper about the opening-closing of borders and in health aid that become important in times of pandemics.
On the economics side, the paper uses a Solow model as in Bonds, et al. (2010) while the literature has moved on to using a neoclassical or even endogenous growth models. This is relevant as it is not possible to make welfare comparisons regarding policies in the Solow model.
The epidemiology parameters and vaccination use a rule of thumb when the economic epidemiology literature is studying optimal policies. The optimal policies are non-linear so the use of rule-of-thumb policies which depend on the capital stock is misleading and does not capture the complexity of how policies change with incidence of the disease and economic conditions.
There is lack of clarity on how disease externality is modeled and dealt with. There is a different disease externality in Gersovitz and Hammer (2003) and Goenka and Liu (2020) but the externality in this paper, as I understand it, is the movement of people across countries. It is not at all clear how an ad-hoc aid can correct it as it does not correct for the marginal distortion caused by mobility.
The main issue is that there is no choice in the model -how investment is done, how policy choices are made, how visitation depends on disease incidence, how vaccination is done, how aid is allocated.
On the epidemiology side it is not clear how the movement of infective and susceptible is being modeled. It should take into account the movement of new susceptibles as well as recovered and recovered across countries. The foreign recovered and vaccinated visitors will change the size of the population in a country so that the fraction of susceptibles (now includes both domestic population as well as visitors) and infectives (same applies) will change. Thus, I think that the equations for the population sizes are missing and the rate of visitation should also be there in the epidemiology equations in the model.

Review report of RSOS-210732
In this paper, authors have considered the spill back of disease of poverty using two country model and discussed how health aid can be helpful to mitigate the externality that comes from the disease. Authors have developed the model, calibrated parameters and performed numerical analysis to illustrate the qualitative aspects of how health aid be helpful in reducing the disease externality. The paper certainly considers an important issue in disease control as well as economic downfall, but it needs some more rigorous work before it should go to publication house.
The major points are following: 1. First of all, I'm little skeptical about the word used in title. the authors have used the word 'spillback'. The 'spillback' has some technical meaning in the theory of Epidemiology. However, it has not been focused or discussed in the context of spillback of the disease in the rest of the paper. The model also does not describe the dynamic 'spillback process'. It gave me a wrong impression and will do for future readers as well. Author may replace it by simpler word like 'cross-border infection' etc.

For example, can authors estimate or calculate what is the potential spillback risk because of the cross-border infection and how much health aid is required to save the country from economic downfall?
What I see presently in the paper is just a qualitative discussion of what affects what.
3. I have also doubt about one conclusion that author made in the paper. They say that high friction affects the GDP of the lower income country more than the higher income country. But I think it depends on that disease intensity in the two countries. For example, here authors do not compute any epidemiological indicator to measure the disease intensity of the two countries like R 0 , the basic reproduction ratio. So, if one considers this basic reproduction ratio different for the two different countries in the prescribed range for this particular infection, the conclusion may be different. Authors definitely needs to consider in their analysis.

The 'introduction' does not seem to be very motivated according to the results that author wanted to discuss in their paper.
So the 'introduction' should be rewritten.
5. In the introduction authors have mentioned diseases like TB, malaria or HIV. I believe the model formulated in the paper is way more simple to describe any of such infections. So, authors should highlight what specific infection they're talking about, which also relates the point 6 below 6. Another major drawback in this paper I see the disparity in timescale of disease and timescale of economic downfall as it shows in figure 1 and in many others. The duration of an outbreak is 20 years minimum in some figures, and it is more than 70 or 80 years. I'm not sure what kind of disease or infection that author had in their mind. This is a major drawback and authors need to rescale in their code and redo all simulations.
7. Some figures have multiple legends, but not reflected in the figure template.

8.
Another important issue is rewriting the calibration process of parameters of the model (in Appendix). Authors have used several functional forms to calibrate their parameters. Although some references have been pointed out, but it requires more details for naive readers.
I would be happy to see the revision taking care of all these points.

RSOS-210732
This paper models the interaction between two countries through tourism mobility. An infectious disease with SIR dynamics is prevalent in each country, and the economic structure is modeled through a Solow growth model so that the savings rate is constant. Modeling the role of interaction between two countries taking into account disease prevalence as well as economic activity in understanding pandemics is important.
Answer: We would like to thank the reviewer for finding the research problem important. Many of the comments and suggested changes from reviewer 1 envision a much bigger, differently focused, and much more expansive economic policy paper. It is difficult to address such comments when the intention of our first paper was to introduce our model and apply it to a health and health policy (not economic) externality context. Our future work will consider many of the ideas and have more emphasis on economic policy considerations.
However, there are some issues in modeling choices that affect what one can learn from the paper about the opening-closing of borders and in health aid that become important in times of pandemics.
On the economics side, the paper uses a Solow model as in Bonds, et al. (2010) while the literature has moved on to using a neoclassical or even endogenous growth models. This is relevant as it is not possible to make welfare comparisons regarding policies in the Solow model.
Answer: We are aware that the current model is a crude depiction of welfare and obtaining accurate welfare comparisons for policy making was not the focus of the modeling exercise. Our model doesn't extend to welfare comparisons while it is a direction in economical modeling of the effect of diseases, it would require adding an optimization step and consumption data and that will require a large change in the work that started as an extension to the work of Bonds et al. (2010). We also added a sentence to the discussion section to indicate the future research direction of including welfare comparisons along the lines of Gersovitz and Hammer (2003) and Goenka and Liu (2020). The additional text is: "Future work will consider the strategic interactions between the two country's health authorities with game theory analysis. Also, our model is scalable which allows us to consider multi-country scenarios to analyze externality occurring between trading networks or trading blocs. It will more closely emulate real world situations about health externalities. More importantly, it is recommended in the future to use neoclassical or endogenous growth models to depict the economic growth of the countries whose households are the main decision makers in investment and disease mitigation, see [12,14]. Other extensions of the current modeling study include investment decisions, policy choices, and aid allocation".
We have also included references: Gersovitz and Hammer (2003) and Goenka and Liu (2020) to the introduction as work on the issue for single countries.
The epidemiology parameters and vaccination use a rule of thumb when the economic epidemiology literature is studying optimal policies. The optimal policies are non-linear so the use of rule-of-thumb policies which depend on the capital stock is misleading and does not capture the complexity of how policies change with incidence of the disease and economic conditions.
Answer: We made assumptions regarding epidemiology and vaccination parameters based on voluntarily vaccination as many diseases like TB in many places, and we did not consider the additional policy implications (e.g. vaccination uptake and hesitancy, etc.). These are great ideas to consider but they are outside the scope of the paper which is intended to be a simple modeling exercise to show the effect of disease externality on the economy and how aids (in the form of vaccine subsidy) can result a change in the effect of the externality. Of course, those are smart new extensions that we can add to our current model. We will consider such extensions in a follow-on manuscript and as part of our future research in to this topic. We added the idea that vaccinations are voluntarily and non-mandatory in many places of the text.
There is lack of clarity on how disease externality is modeled and dealt with. There is a different disease externality in Gersovitz and Hammer (2003) and Goenka and Liu (2020)  So externality is the economic loss as well as infections incurred by country 2 due to the spread of disease in country 1 because of country 1 's incapability of protect its people through economic prosperity that gives rise to better hygiene, nutrition and treatment ( Figure 1 e and f shows a proof). Mobility constitutes the medium of the spread of the disease, and air in many environmental externality problems, it cannot not be always decreased through higher friction (Figure c and d as a proof). It could be however abated through health aid in the form of vaccination.
To better clarify this point we also explained the concept of externality in view of the aforementioned paper (and also added it as a reference) with the following sentence that is added to the introduction: "The term externality is defined in a number of ways. Externality is a result when an agent produces or consumes a good or service that causes a cost or benefit on other parties who are not involved in this transaction [7]. In terms of disease spread, it could be identified through people's risk of infection due to other people's behaviors [1]." (Alvarez et al., 2020 reference).
The main issue is that there is no choice in the model -how investment is done, how policy choices are made, how visitation depends on disease incidence, how vaccination is done, how aid is allocated.
Answer: We thank the reviewer for proposing those interesting extensions to the current modeling approach. This is an initial paper that focuses on the effect of health aid to remedy externality in contrast to closing borders, especially if there are mutual benefits. We added a sentence in the discussion section to express the need to expand the model to address those points for future research efforts. We are also considering developing a follow up paper that will address these points (investment, policy choices, etc.).
The sentence is: Future work will consider. … Other extensions of the current modeling study include investment decisions, policy choices, and aid allocation.
On the epidemiology side it is not clear how the movement of infective and susceptible is being modeled. It should take into account the movement of new susceptibles as well as recovered and recovered across countries. The foreign recovered and vaccinated visitors will change the size of the population in a country so that the fraction of susceptibles (now includes both domestic population as well as visitors) and infectives (same applies) will change. Thus, I think that the equations for the population sizes are missing and the rate of visitation should also be there in the epidemiology equations in the model.
Answer: The reviewer makes a good point. The interaction between the two countries' citizens is modeled using the Newton's law of attraction. The number of visitors to the total population cannot be of significant alteration to the total population since visitations happen both ways and are transient in nature. Also, there are high (peak tourism) and low (off peak) seasons during the year and so we take the assumption that, on average over the year, there will be no significant change in the total population made by visitation of one single country to another. Also, it will be distributed over the whole country and we doubt that it will be of practical influence. Note that visitation here is reciprocal and is accounted for one single country in our model.

Review report of RSOS-210732
In this paper, authors have considered the spill back of disease of poverty using two country model and discussed how health aid can be helpful to mitigate the externality that comes from the disease. Authors have developed the model, calibrated parameters and performed numerical analysis to illustrate the qualitative aspects of how health aid be helpful in reducing the disease externality. The paper certainly considers an important issue in disease control as well as economic downfall, but it needs some more rigorous work before it should go to publication house. The major points are following: 1. First of all, I'm little skeptical about the word used in title. the authors have used the word 'spillback'. The 'spillback' has some technical meaning in the theory of Epidemiology. However, it has not been focused or discussed in the context of spillback of the disease in the rest of the paper. The model also does not describe the dynamic 'spillback process'. It gave me a wrong impression and will do for future readers as well. Author may replace it by simpler word like 'cross-border infection' etc. Answer: We agree with the reviewer, and we have edited the title to remove the term "spillback." We changed it to "cross-border infection." 2. For example, can authors estimate or calculate what is the potential spillback risk because of the cross-border infection and how much health aid is required to save the country from economic downfall?
What I see presently in the paper is just a qualitative discussion of what affects what. Answer: We added some quantitative results in figures 7 and 8 besides those in figure 6 and including a new paragraph in between those figures. They are bolstering the main finding of the paper that swift and higher levels of aid can save both countries almost as much as when decreasing risk of infection, by for example social distances that are not reasonable over decades. 3. I have also doubt about one conclusion that author made in the paper. They say that high friction affects the GDP of the lower income country more than the higher income country. But I think it depends on that disease intensity in the two countries. For example, here authors do not compute any epidemiological indicator to measure the disease intensity of the two countries like R0, the basic reproduction ratio. So, if one