Model

We first wanted to learn how we can use models and what exactly modeling is, so we organized and participated in a modeling workshop with U of L Biochemistry PhD Candidate Elizabeth Trofimenkoff. She explained how we can use math to model many different aspects of life and molecular biology.

For our project this year, we are constructing a device to test for bovine respiratory disease (BRD) in cattle. Along with testing, knowing how this respiratory virus spreads and its timeline is important. This is also important in testing the feasibility of our device. We have created a Python model to model the spread of BRD around a feedlot. To create this model, we used an SIR approach. SIR stands for susceptible, infectious, and removed/recovered individuals. Susceptible individuals are those who are yet to be infected. When they contact infected individuals, they contract the disease and become part of the infectious compartment. Infected individuals are those who have been infected and can infect susceptible individuals. Removed, immune, or deceased individuals are individuals who have been infected and recovered from the disease or died from it. The number of deaths is negligible with respect to the total population.

Beta represents BRD's infection/ transmission rate (how easily it spreads). It is always between 0 and 1. This means that for every 1 infected cattle coming into contact with a susceptible cattle, it catches the disease. R stands for the number of recovered cattle. N represents the total population of cattle in a feedlot. H (gamma) represents the amount of time the cattle are affected for/ recovery rate (how long before they are recovered). The incubation period is the time before signs of BRD show within a cattle, which is 3-5 days. Cattle become infectious on days 7 - 10 of contraction.

Figure 1. A predictive model for the spread of BRD pathogens in a feedlot. The initial parameters were for 216 beef cattle over 200 days. Using 1./14 days as gamma. Gamma describes the duration of infection. 0.25/1 as Beta. Beta refers to the contact rate and how easily BRD spreads between cattle. Infection levels were monitored one time each day.

A recurring inquiry from judges in various competitions throughout the year has been the rationale for utilizing Bo-FIND as an alternative to traditional polymerase chain reaction (PCR) testing for bovine respiratory disease (BRD). Beyond the financial burden and inconvenience of veterinary consultations, PCR testing is notably time-intensive. BRD outbreaks typically manifest within the initial weeks following cattle arrival at feedlots, with morbidity often peaking within 7-10 days post-arrival. Our model demonstrates that cattle can contract BRD and become infectious within the first 13 days of exposure. By the time farmers observe symptomatic cattle and initiate testing, PCR results may take several days to return, during which BRD can proliferate extensively throughout the feedlot population. Implementing a rapid detection device as cattle disembark from transportation vehicles offers significant time and cost efficiencies. Farmers can ascertain within hours whether newly introduced cattle are infected, enabling immediate action to mitigate disease spread. This approach not only eliminates the need for PCR testing but also allows farmers to address the issue autonomously, without third-party involvement, thereby optimizing both financial and operational resources.

Our device is a key component of our project, and we wanted to create a model to determine its probable lifespan. The graph displays the decrease in efficiency over twenty years with the probability of survival. To create the individual parameters for the graph, we imputed the lifespan of each separate device component into our code. The type of survival analysis model we created was a Kaplan-Meier model. A survival analysis graph is one used for statistical analysis to map out the expected duration of time before an event occurs. This event can be death or the failure of a mechanical system. In the Kaplan-Meier curve, the x-axis represents time and the y-axis is the proportion of survival. In relation to our graph, the y-axis at time zero represents one hundred percent of device parts functioning without any events occurring. The solid line, which resembles a staircase, indicates the continuance of event contingencies. Each time this solid line displays a vertical drop, an event has occurred. This might be the failure of a specific system part or a reduction in its speed efficiency. This model provides buyers and consumers insight into factors influencing our device's lifespan. It is crucial to show the feasibility of our device in terms of time and lifespan.

Figure 2. The probable lifespan of our device over 20 years. In the first two and a half years, the efficiency and lifespan of the device will drop by 50%. Over eleven years, the device will maintain a steady efficiency rate before it will slowly stop working in the last five years as the probability of its survival decreases significantly, as shown in the graph.

In our project, we aimed to develop financial models, including a break-even analysis that illustrates the number of BRD testing kits we need to sell to achieve profitability. We established a selling price of $117 for each kit, which includes the necessary materials to test one cattle. This price point was derived from the following cost breakdown: $15 for wet lab materials, $58 for the Arduino kit, $17 for chitosan, the material used to encase our heating device, and $0.023 for centrifuge tubes. We applied a 30% markup to these costs to ensure a profit margin. Additionally, we accounted for fixed costs amounting to $1,500 to cover labor and other expenses related to production. Furthermore, we designated a variable cost of $100 per product to accommodate unforeseen expenses such as shipping and packaging.

Components	Cost (CAN)
Wet lab materials	$15
Arduino kit	$58
Chitosan plastic	$17
Centrifuge tubes	$0.023
Subtotal	$90.023
30% markup	$26.977
Total Selling Price	$117

The resulting graph indicates that we must sell 88 units before we begin to realize profits. This figure is particularly significant as we believe there is a strong niche market for our product, with potential customers who would be willing to make a purchase. The insights gleaned from this analysis provide us with a clear understanding of the financial landscape we may encounter while marketing our BRD testing kits.

Figure 3. A Predictive break-even model if we were to sell our product at $117 (CAD) with a $1500 fixed cost. Break-even in profit margins occurs at 88 units sold. Before this point, there is no profit; after the break-even point, we begin to yield.

Figure 4. A predictive model showing a $3 (CAD) decrease per 2 units of Bo-Find sold if 36 devices are sold at $117 each.

In this equation, the number 88 represents the initial product quantity sold, while 117 stands for the initial cost per unit. The relationship described suggests that for every $3 decrease in the price, an additional two units of the product are sold. This reflects a common economic principle where lowering the price leads to increased sales. The quadratic equation (88+2x)(117−3x) models this relationship, where x represents the number of changes. Four price decreases will yield maximum profits while still staying above production costs and allowing us to make a profit. This model is important in determining the most optimal price for our product which in theory should be 102 dollars which is achievable if our product can get past the break-even of 88 units and start making a profit.

The graph of this equation shows how sales and revenue are affected by price adjustments. Initially, sales increase as the price decreases, but due to the parabolic shape of the graph, there is a point where lowering the price further begins to negatively impact overall revenue. This happens because our sale price then drops below 60 dollars and we lose money selling while there is more demand for the product.

Our iGEM team, based in Lethbridge, Alberta, Canada, has developed a project aimed at supporting our province's farmers and agricultural industry. As we've developed the Bo-FIND design, we've recognized the critical need to consider Alberta's diverse climate and its potential impact on our device's performance. Alberta experiences extreme temperature fluctuations, ranging from below -20°C in winter to over 30°C during the summer months. These environmental conditions prompted us to investigate their effects on Recombinase Polymerase Amplification (RPA) efficiency, a key component of our device. To visualize these effects, we created a model comparing average temperature and humidity during Alberta's four seasons to optimal RPA conditions.

Our graph displays temperature (°C) and humidity (%) as bar charts for hi each season, with a red line representing the calculated amplification success rate. The optimal condition (37°C, 50% humidity) yields a 100% success rate. Winter (-20°C, 35% humidity), Fall (5°C, 35% humidity), and Spring (20°C, 48% humidity) show lower success rates of 0.76, likely due to suboptimal temperatures. Summer conditions (30°C, 43% humidity) maintain a high success rate of 0.95, as the temperature remains within a favorable range.

Figure 5. The seasonal performance of recombinase polymerase amplification (RPA) in Alberta, Canada. Efficiency varies across average temperatures of Optimal (37℃), Winter (-20℃), Summer (30℃), Spring (20℃), and Fall (5℃).

Our analysis reveals that even in less-than-ideal conditions, RPA maintains a relatively high success rate (above 0.75). This finding is significant as it demonstrates that our device, Bo-FIND, can function effectively across Alberta's varied climate zones, ensuring its practicality for farmers throughout the province despite seasonal changes.