Activities 1 to 3 are simpler than activities 4 and 5, which are linked to each other and to Activity 3, and require more time and effort.

    1. Important terms. Be sure you have each of the terms clear in your mind. If you don’t, go back and read the background information.

- Epidemic.

- Epiphytotic.

- Negative epidemic.

- Endemic.

- Infection cycle.

- Monocyclic, polycyclic and polyetic epidemics.

    2. Monocyclic and polycyclic diseases

    2.1. Break up into groups (approximately 2-5 people, but possibly more).

    2.2. For each group, give the concept and 2 examples, at least one for potato, for each type of disease (monocyclic and polycyclic). Use one card for each type of disease.

    2.3. For each type of disease, write the equation (linear or exponential) which describes it. Use a separate card for each equation.

    2.4. A different representative of each group presents the results.

    3. Epidemiological basis of disease management

    3.1. Install the program Plant Disease Development.

    3.2. Start the program, do the simulation exercises outlined in the Epidemiology course and answer the questions.

Form groups of 2 or 3. For each group, list all the tactics you can think of in your context to reduce epidemiological parameters for potato late blight (LB) using the exponential model (x = x0 ert, where x is severity, x0 is initial severity, e is the base of natural logarithms, r is the apparent infection rate, and t is time). Use a separate card for each strategy (reduce x0, reduce r, or reduce t) and list several tactics on each strategy. For each tactic, estimate the reduction on the parameter value, e.g., use of a resistant cultivar reduces r in 30%. Select the 3 most important tactics for each strategy and complete Table 1.

Table 1. Strategies and tactics to manage potato late blight as predicted by the logistic model.

* Principles of disease management: avoidance, exclusion, eradication, protection, resistance, and therapy.

    3.4.   Each group picks a representative to present the results. Group discussion.

    4.Selection of an appropriate model (logistic or monomolecular) for describing disease progress data

This activity can be done with data provided here or with data brought by the participants that were previously used in Activity 1 of the training unit Summarizing the epidemic.

Work on the same groups of the previous activity and assume you don’t know that LB is a polycyclic disease. You have obtained severity data of 2 LB epidemics in the field as shown in the EXCEL file Analytical models (student)[1][1][1] and want to summarize and analyze the progress curves of these epidemics. The parameter that you selected is the infection rate, which is a parameter of several models of disease progress, among them the logistic and the monomolecular. Your job is to estimate the infection rate and the other parameters for these models and decide which model is the best to summarize the epidemics based on visual comparisons of observed and predicted progress curves.

    4.1. In the file Analytical models (student), Sheet1, calculate the monomolecular and logistic transformations of the severity values. The logistic transformation is also known as ‘logit’. Since severity (x) is expressed as percentage, use equation 1 for the monomolecular and equation 2 for the logistic transformations:

Monomolecular transformation = ln(100 / [100 – x])         [1]

Logistic transformation = ln(x / [100 – x])                          [2]

Be careful not to include severity values of 0, to replace 100 by 99 in the first severity reading with 100, and not to include the remaining severity readings with values of 100.

    4.2. The rates of disease increase for both models will be automatically calculated in column W. Check how these are calculated.

    4.3. Go to Table A (the tables and figures in the file Analytical models (student) are represented with capital letters) and complete the parameter values for both models. Note that the initial inoculum is the average of the severity values in the first reading divided by 100.

    4.4. In Table B, calculate the predicted severity with both models. For the monomolecular model use the following equation:

Where xMon is the predicted severity with the monomolecular model; Q is initial severity; exp is the function that EXCEL uses to raise the base of the natural logarithms (e) to the power of a given number; R is the infection rate; and t is time. For the logistic model use equation 4:

    4.5. The observed and predicted disease progress curves will be automatically graphed       in Figure B.

Assess visually the goodness of fit for the predictions made by each model in both epidemics.  

Based on that, decide which model is the best to summarize the epidemics.

    4.6. Each group picks a representative to present the results. Group discussion.

    5.Using an analytical plant disease model

The logistic model with the parameters for the epidemic of cultivar Amarilis with no fungicide of exercise 4 will be used to demonstrate how an analytical plant disease model can be used to explore disease management options. This exercise is similar to exercise 3, but here we will compare different epidemics in a quantitative manner using the area under the disease progress curve (AUDPC) as epidemic descriptor. In addition, you will learn how the Plant Disease Development program actually works.

    5.1. Work on the same groups of the previous activity. Copy your results from Table 1 into the   pink row of Table C in the file Analytical models (student), Sheet2. Also select the best tactics for reducing x0, r, and t.

    5.2. The values of Table D will be automatically calculated. Note that the baseline parameter values (from the LB epidemic on cultivar Amarilis with no fungicide) are decreased according to the values of Table C. These ‘reduced’ values are in the yellow cells. The parameters of each tactic are used in Table E to generate predicted severity values with the logistic model. The AUDPC of each simulated epidemic and the reduction on AUDPC with respect to the ‘baseline’ epidemic are also calculated. Note, since there are severity values for each day, AUDPC is the sum of these severity values. Also note how the predicted severity values are calculated (see equation 4). This is how the Plant Disease Development program works. The predicted diseases progress curves of 2 epidemics (baseline and another resulting from the application of a LB management tactic) are also shown. You can graph others epidemic by doing the following: (i) right-click on the curve you want to change, you will see that 2 columns of data are highlighted: one corresponds to the values of the x axis (days after emergence) and the other to those of the y axis (predicted severity); (ii) move the cursor carefully onto the y-axis column until the highlighted border becomes darker; (iii) by keeping pressed the right bottom of the mouse, move the highlighted part to the column corresponding to the epidemic you want to graph.

    5.3. Complete Table 2 with your results. Estimate the efficiency of each tactic by dividing the reduction in AUDPC (b) by the reduction in the parameter value (a).

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[1] If you are a facilitator, you may want to use file Analytical models (facilitator).

Table 2. Efficiencies of LB management tactics as predicted by the logistic model. The reductions on the parameter values for each tactic are estimations.

      5.4. Each group picks a representative to present the results. Group discussion.