Economic Model

Overview

The spread of FOC TR4 is widely recognized as a potential threat to the banana economy as prevention measures for such disease remain highly undeveloped. We hope to use a predictive economic model to yield a better understanding of how the Fusarium Wilt pandemic might impact the economy as it continues to spread, and also examine how our designed liquid inoculant (referred to as prototype bellow) can buffer the problem if it's implemented by farmers.

We established two models: a macroscopic model focusing on how the banana market as a whole suffers from economic losses as FOC TR4 continues to spread, and a microscopic one that estimates the losses of individual farmers once the pandemic hits their farmlands. The results of the models can serve as a reference for hardware, implementation, marketing, and other human practice efforts, providing a dynamic insight into the utility of our prototype.

Methods

Scope & Purpose

In order to generate a comprehensive conclusion, it's beneficial to establish different models in order to provide a multi-perspective analysis. In our case, we established two economic models that analyze on different scales, each having their own exclusivity in perspective and usage.

The consideration of disease spread rate is the critical aspect that separates the macroscopic model from the microscopic one. The macroscopic model takes in consideration of disease spread rate in order to provide a general prediction of how the banana market would be damaged by FOC TR4 as it spreads. The microscopic model, however, disregards the principles of spread, as it only examines Fusarium Wilt-induced damage on small, individual farmlands.

The non-overlapping scope allows the two models to serve unique purposes. The macroscopic model can serve as a proof for our prototype’s effectiveness in inhibiting FOC TR4 spread in a local environment, and examine how the inhibited spread helps ease the overall economic damage. On the contrary, the microscopic model provides a microeconomic approach for forecasting the individual farmers’ incentive for purchasing our prototype by predicting how farmers could potentially benefit from it, and generates insight as to how the prototype could be marketed if normally manufactured and sold.

Subject of Study

For simplicity, the subject of investigation of our model would be set to our own country, Taiwan. The reason for this choice is that data relating to the Taiwanese banana economy is well documented due to the economic importance of bananas in the agricultural market. Additionally, the economic importance of bananas in Taiwan makes Taiwanese banana industry an ideal candidate for modeling. Our study essentially serves as a proof of concept; the framework and models used throughout this study should also be able to apply to other countries.

Macroscopic Model: Analyzing FOC TR4-induced Local Economic Damage Over Time

In the macroscopic model, we aim to figure out how the FOC TR4 spread burdens the local banana economy. In order to quantify the damage caused by the Fusarium Wilt pandemic, we need to establish a method that predicts how FOC TR4 would locally spread if FOC TR4 is instantly introduced and established in a new environment.

We modified an established method ((Cook et al., 2015)) for quantifying disease damage caused by the Fusarium Wilt pandemic. The total economic damage caused by FOC TR4 is weighed by five parameters: area of spread, infection density, number of infection sites, price of bananas, and survival rate.

\begin{equation} a_t = 4D\pi rt^2 \end{equation}

Equation 1, Area of Spread. The area of spread, notated by a, is calculated by considering the diffusion speed of FOC TR4. It is assumed that FOC TR4 would eventually reach a maximum diffusion rate of 2√Dr, where D is the diffusion coefficient of FOC TR4 (in m²/ year) and r is the growth factor (per year), and that FOC TR4 would spread equally in all directions with the same diffusion rate. The speed of diffusion is multiplied by time to yield the distance TR4 can travel relative to its originally established site, and the overall circular area of an expanding infection site at a given year after initial establishment can be estimated.

\begin{equation} N_t = {K N^{min} e^{rt} \over K + N^{min} (e^{rt} - 1)} \end{equation}

Equation 2, Infection Density. The infection density (in kg of bananas/m^2), notated by N, is assumed to grow in a logistic curve, and the curve is constructed in consideration of the maximum FOC TR4 infection density a given area of land can support (notated by K), and the minimum infection density required for FOC TR4 to continue to spread (notated by N min).

\begin{equation} S_t = {S^{max} S^{min} e^{\mu t} \over S^{max} + S^{min} (e^{\mu t}-1)} \end{equation}

Equation 3, Number of Infected Sites. The number of infected sites (also known as satellite infection sites) is assumed to follow a logistic growth curve, taken in consideration of maximum and minimum possible infection sites in a given region. This parameter, noticeably, is the only location-dependent parameter out of the five.

\begin{equation} M_t = S_t {(a_t N_t)} \end{equation}

Equation 4, Total Mass Infected. By multiplying the three parameters, the total mass of bananas that are infected by FOC at a set period of time after disease establishment, notated with M, can be estimated. In order to estimate the overall economic loss resulting from the infected bananas, factors such as the price of banana per unit mass and banana’s survival rate under FOC TR4 infection would need to be further considered.

The death rate of banana under FOC TR4 infection needs to be considered, since some banana species have natural resistance for FOC TR4 and wouldn’t immediately die or become unsellable upon infection. The percentage of yield reduction is notated with Y. It is assumed that directly multiplying the original yield reduction rate with the additional survival rate that our prototype provides would yield the overall reduction rate when the prototype is implemented. We also assume that the prototype is implemented in all banana farmlands in Taiwan in order to calculate the best possible scenario for economic reduction.

The price of bananas is reasonably predicted to be steadily increasing due to factors such as inflation and decrease in production due to TR4 infection, as the trend can also be seen in past data on banana retail price in Taiwan. @RISK analysis is performed to calculate predicted price of banana by taking price data of banana from the past 20 years to provide a predictive trend of banana retail price.

\begin{equation} d_t = Y_tP_t M_t \end{equation}

Equation 5, Total Market Loss. By multiplying the mass of bananas infected, survival rate of bananas under FOC TR4 infection, and the predicted price of bananas, the overall economic loss in banana market due to FOC TR4 infection in any given year after original establishment can be predicted, and a damage over time graph can be constructed.

Microscopic Model: TR4 Economical Damage On Individual Farmers

Mass production of our prototype would be required if we are aiming to solve the problem of the Fusarium Wilt pandemic on a global scale, therefore we need to consider a marketing plan for our prototype once it becomes a consistently manufactured and sold product.

In order to establish a marketing plan, it is essential to quantify the demands of consumers and the producers’ incentive of production, so we established a microeconomic model to assist us with understanding the potential market dynamics of our prototype. By combining the farmers’ net revenue increase from implementing the prototype and the production cost of the prototype, we would be able to determine a price range for the prototype to aid our marketing strategy.

\begin{equation} {\text{kg of bananas} \over \text{unit area}} \times {\text{Additional survival rate provided by prototype (\%)}} \times {\text{price} \over \text{kg of banana}} = \text{Marginal net revenue increase} \end{equation}

Equation 6, Marginal Net Revenue Increase. The marginal net revenue increase per year from implementation can be modeled with the above equation. The equation essentially predicts how much additional revenue the farmers can earn by selling the additional bananas protected by our prototype. It's important to understand how the farmers’ revenue would increase, since it is highly associated with the prototype’s cost. If the cost of a prototype is higher than the net revenue it can generate, then the farmers won’t have the incentive to purchase it. Thus, the net revenue increased from implementing the prototype can be interpreted as the maximum possible price of the prototype.

In addition to analyzing farmers’ benefits in implementing the prototype, the prototype’s cost of production is also taken into consideration for pricing. The price of production is estimated to determine the lowest possible price of the prototype, in order to calculate the farmers’ maximum possible profit from implementing it.

Once we have developed a pricing range for our prototype, marginal analysis of farmers’ profit would be made to predict how the farmers can profit from purchasing the prototype. The net revenue increase from implementation and the price of the prototype will be taken into consideration when calculating the annual and total profit of banana farmers.

Obtaining Parameters

Predicted Banana Retail Price

The future retail price of bananas is predicted by using @RISK, a software whose primary usage is to use historical data to provide forecasts. The annual average price of Taiwanese bananas for the past 20 years (2012-2022) is inputted, and a future trendline is generated by using first order differencing. The mean of the predicted price represents the future retail price of bananas in our model. The price of bananas can be reasonably predicted to accumulate naturally due to factors such as inflation and decrease in production. However, such factors would not be specifically integrated into the mathematical model due to their natural complexity and unpredictability.

The timeframe of investigation in our study is chosen to be 30 years starting from 2022 for simplicity. However, the timeframe of investigation can be set to anytime in the future. As long as the historical price data is sufficient, the banana retail price during the timeframe can be estimated by using the same method.

Additional Survival Rate of Bananas Induced by Prototype Under TR4 Infection

Since the subject of modeling is Taiwan, the resistance of the most popular banana species, Tai Chiao No.5, would be considered to represent the overall resistance of Taiwanese banana population. The death rate of Tai Chiao No.5 is experimentally determined to be roughly 20 percent (Lee et al., 2006).

The additional resistance provided by our prototype is predicted by analyzing chi18H8’s ability to inhibit the growth of FOC TR4 when cocultured (Hjort et al., 2013). Engineered chitinase-secreting E.coli are stamped around in a FOC TR4 culture inoculum for the experiment group, while non-modified E.coli cells are used for the control group. The radius of the FOC TR4 culture for each group is compared to come up with an estimated inhibition percentage of 35.1%, and a regression model (Meriem et al., 2022) is utilized to relate the inhibition percentage to overall disease reduction. The estimated disease reduction for our prototype is 32% (68% death rate).

The overall death rate of Tai Chiao No.5 under the protection of our prototype is estimated by multiplying the original death rate, 20%, by the death rate under prototype protection, 68%, yielding an overall death rate of 13.6%. By subtracting the original death rate of Tai Chiao No.5 by the combined death rate of the species under prototype protection, an additional survival rate of 6.4% is calculated.

Parameters for modeling spread (Macroscopic model)

Below are the parameters utilized in the macroscopic model, proposed by Drenth (Cook et al., 2015). Noticeably, the parameters are used to study the Australian Fusarium Wilt pandemic, therefore the location-specific parameter, maximum number of satellite infection sites generated, doesn’t necessarily apply to our model. However, due to the lack of literature regarding the parameter, we decided to temporarily use the proposed value instead. If a more location-specific approach for obtaining the parameter is established, we would be able to produce a much more accurate prediction of FOC TR4 spread specifically for Taiwan.

Production Per Unit Area (Microscopic Model)

Mass of bananas produced per unit area is estimated by taking the total weight of the banana produced annually divided by total area of banana plantation in hectares (Taiwanese council of agriculture, 2011) . It is assumed to be averaged instead of using a predictive curve, taking in consideration the maximum capacity of plantation. The averaged production per unit area is 14686 kg of bananas per hectare of plantation.

Production Cost Estimation (Microscopic Model)

By comparing the costs of similar products with our prototype, we came up with an estimated cost of 733 NTD per liter of prototype. The frequency of implementation is estimated to be 18 times per year, with every time using a 0.25 liter prototype, therefore the annual requirement for implementation is 5 liters of prototype per year. With one litter costing 733 NTD, the annual cost for prototype implementation is estimated to be 4,000 NTD. For more information on sources and calculations, see Implementation Page.

Results

Macroscopic Model

The predicted price, number of infection sites, infection density, and the area infected is shown in the table below, with year 1 being 2022. The 4 parameters and the death rate of bananas under FOC TR4 infection are combined to calculate the annual profit decrease.

Microscopic Model

The net revenue change under prototype implementation is predicted to be gradually increasing as infection period lengthens. This is due to the retail price of bananas increasing as an effect of decreasing production of bananas in the local market. The net revenue is predicted to be around 22,000 NTD (705 USD) per hectare of plantation for the first few years, and would eventually increase to an amount of 37,000 NTD (1185 USD) per hectare at the end of the investigation timeframe.

By subtracting revenue by production cost, the marginal net profit per hectares of land for each year is calculated. The marginal revenue for each year is then accumulated to calculate the total profit. At the end of the 30 year investigation timeframe, an estimated total profit of 709,000 NTD (22,300 USD) can be gained per hectare of farmland.

Discussion

Using the economic models, we were able to gain insight into how severe an economic recession due to the Fusarium Wilt pandemic can be, and how our prototype could be implemented to ease the economic crisis. We first analyzed the banana market at a large scale, taking into account the FOC TR4 spread rate, and came up with an estimate of how the Taiwanese market as a whole would suffer from losses. The results suggest that FOC TR4- induced damage can amplify rapidly as the infection period lengthens, and at the 30 year mark, an estimated amount of 680 million NTD of revenue (22 million USD) would be reduced from the local market. As the damage increases, the significance of our prototype also increases, as it is estimated that the prototype would save 140 million NTD of revenue (4.5 million USD) at the 30 year mark. It can be considered that the effects of our prototype can significantly buffer the economic losses, therefore achieving our goal of buffering Fusarium Wilt pandemic impact and buying time for more predictive measures to be implemented.

While typical economic models only analyze the general trend of disease-induced economic damage, the macroscopic model takes into consideration the species behavior and its interactions with the environment, providing a much more robust prediction of the disease’s impact, as well as the degree of regulation that can be achieved through means of inhibitive measures. Our model would be much more ideal for referencing when it comes to policy making in disease containment, since it is oftentimes difficult for policy makers to consider disease impact with respect to time, space, and other variables that are typically hard to predict. Our model could provide information regarding such variables in a much more precise manner.

The second model then examines the maximum possible profit the farmers can generate per hectare of farmland by implementing our prototype. The maximum net revenue gained from implementing our prototype per hectare of land and the production cost of the prototype were then combined to provide an analysis of net profit per hectare of land. The profit for the first few years is estimated to be 20000 NTD (630 USD), and the profit for the farmers during the 30th year mark is roughly 32000 NTD (1000 USD). The cumulative profit for the 30 year investigation timeframe is estimated to be 757000 NTD (24000 USD).

The economic models can prove the significance and potential impact of our project, as we are trying to solve an urgent problem in the field of agriculture. The frameworks we utilized can be referenced in future risk analysis on similar diseases. If alternative methods for inhibiting FOC TR4 spread are established in the future, our model can also be used to predict the market dynamics of the prototype if implemented.

Conclusion

In brief, two bioeconomic models were created to analyze FOC TR4 induced economic damage for a duration of 30 years, and the significance of our prototype in easing the losses were proved. By the 30 year mark, a maximum amount of 140 million NTD of revenue (4.5 million USD) would be saved by implementing our prototype, therefore effectively serving as a buffer for economic impact caused by the Fusarium Wilt pandemic.

The benefits of farmers using our prototype are analyzed by considering the production cost of the prototype and the marginal benefit of implementing the prototype. It is predicted the cumulative profit would reach 750 thousand NTD (24 thousand USD) for each hectare of farmland. It can be concluded that our prototype has a solid ability to alleviate the economic crisis caused by Fusarium Wilt pandemic, and is worthy to be invested and mass produced in the future.

Limitations

Due to the natural complexity of economics, our model is designed to take a generic view on the banana industry and its future, therefore we neglected overly specific factors when modeling. When making the assumptions, we assume that the current status of the market, such as factors of production and demands, would stay consistent throughout the investigated time frame in order to prevent from possibly over analyzing and overfitting data. We believe that such assumptions are specifically valid when conducting models on agricultural markets. In comparison to many other markets in an economy, agricultural markets tend to be more stable due the aid of international policies for keeping the market transparent and predictable (OECD, n.d.). Such stability can suggest that what occurs in the current market would most likely apply to the future, therefore we wouldn’t need to overly specifically investigate the details of the market dynamics.

References

Cook, D. C., Taylor, A. S., Meldrum, R. A., & Drenth, A. (2015). Potential economic impact of Panama disease (tropical race 4) on the Australian banana industry. Journal of Plant Diseases and Protection, 122(5/6), 229–237. Link to Source

Hjort, K., Presti, I., Elväng, A., Marinelli, F., & Sjöling, S. (2013). Bacterial chitinase with phytopathogen control capacity from suppressive soil revealed by functional metagenomics. Applied Microbiology and Biotechnology, 98(6), 2819–2828. Link to Source

Khalifa, Meriem, Rouag, Noureddine & Bouhadida, Mariem. (2022). Evaluation of the Antagonistic Effect of Pseudomonas Rhizobacteria on Fusarium Wilt of Chickpea. Agriculture. Link to Source

Lee, S.-Y., Chiu, T.-H., & Su, Y.-Y. (2006). Tai Chiao No.5 -TC3-1035 species synopsis. OECD. (n.d.). Predictability and transparency - The OECD’s 4 keys to #resilient supply chains present analysis and evidence in response to unprecedented disruptions to international trade, in pursuit of #sustainable and #inclusive recovery. Www.oecd.org. Link to Source

Taiwanese council of agriculture. (2011). Kmweb.coa.gov.tw. Link to Source