A Population-Dynamics Approach to Assess the Threat of Plant Pathogens as Biological Weapons against Annual Crops

In recent years there has been considerable concern expressed in the scientific and popular literature about the threat of biological terrorism (Simon 1997, Henderson 1998, Abelson 1999, Atlas 1999, Osterholm 1999, Stone 2000, Hardy 2001, Stimson Center 2001). This general interest had been propelled by US executive orders on weapons of mass destruction, White House initiatives on biological and chemical weapons preparedness (White House 1994, 1998a, 1998b, 1998c, 1999a), and the release of information from the former Soviet Union on the extent of biological weapons research conducted during the cold war (Alibek and Handelman 1999, Tucker 1999). Obviously, this concern has intensified since the tragedies of September 11, 2001 (Lawler 2001). Much attention has been directed toward the use of pathogenic microorganisms as biological weapons against humans, but there has been growing awareness of the potential use of microbes as weapons against crops as well (MacKenzie 1999, Rogers et al. 1999, Schaad et al. 1999, Yang and Sanogo 2000), especially in view of information that has come to light concerning Iraq's past efforts to develop biological weapons against crop plants (Whitby and Rogers 1997). The impact of plant diseases on agriculture is immense. In the United States, for example, annual total losses due to crop diseases are estimated at over $30 billion, with 65% of that amount attributed to introduced (invasive) microbes (Pimentel et al. 2000). Economically important pathogens continue to be accidentally introduced, some with very large economic consequences (Bandyopadhyay et al. 1998, Gottwald et al. 2001). Although, to our knowledge, plant pathogens have never been deliberately introduced into US crops as an act of warfare or terrorism, there is concern that this and many other countries are vulnerable to such acts of aggression (Kadlec 1995, Horn and Breeze 1999, Pearson 1999). The chances of a given plant pathogen being used successfully as a biological weapon involve, among other things, ease of production, storage, and delivery, and then the fate of the introduced pathogen once it is introduced into a susceptible crop (Schaad et al. 1999). This article is concerned with assessing the risk of the latter, including accidentally introduced plant pathogens (Yang et al. 1991, Ruesink et al. 1995, Schmitz and Simberloff 1997, Enserink 1999), a key component of the Executive Order on Invasive Species (White House 1999b). The Animal and Plant Health Inspection Service (APHIS) of the US Department of Agriculture uses several variations of generic risk-assessment methods to determine the risk of certain plant pathogens (and other pests) being nondeliberately introduced, spreading, and causing economic or other consequences (Orr et al. 1993). This approach does not explicitly or formally deal with the population dynamics of potentially introduced organisms in assessing risk, making it difficult to generate general principles of disease development. Theoretical epidemiology does provide a means, however, based on population dynamics, of predicting the outcome when a pathogen is introduced into a susceptible host population (Mollison 1986, Anderson and May 1990, Diekmann et al. 1990, van den Bosch et al. 1999). This approach has been most extensively used in studying diseases of animals, and especially people; a considerable amount of research with plant epidemics also has been done (Campbell and Madden 1990, Swinton and Gilligan 1996, Gilligan and Kleczkowski 1997, Gilligan et al. 1997). In fact, nearly 40 years ago Vanderplank (1963) outlined the epidemiological principles relevant for assessing the threat of plant pathogens as biological weapons. A common feature of plant epidemics is that plants can become infected at any time by contacts between disease-free plants and (a) inoculum produced during past epidemics or in epidemics in other host populations (known as primary infection) or (b) inoculum produced by infectious plants in the current epidemic (known as secondary infection) (Campbell and Madden 1990). A key parameter in predicting several features of epidemics is the basic reproduction number, R0 (Diekmann et al. 1990), which is defined as the mean number of new infected individuals that results from one infected individual introduced into a susceptible (disease-free) host population (over the lifetime of the infectious individual). R0 must exceed 1 for disease invasion and persistence (Mollison 1995): The epidemic will not die out when each diseased individual leaves, on average, more than one new diseased individual. The magnitude of R0 can be used to determine final epidemic size (either abundance or proportion of diseased individuals in the population), provided there is sufficient time for either a steady state to be achieved (if there is host growth) or an asymptote to be approached (for nongrowing host). Host growth can refer to changes in either the numbers of host individuals or the amount of host tissue available for infection. Thus, for long-lived perennial plant species with continuous disease development, current epidemic theory can, in general, be used to predict epidemic outcomes from accidentally or deliberately introduced pathogens (Jeger and van den Bosch 1994, Swinton and Gilligan 1996, Madden et al. 2000). However, most major crops are annuals (Hanson 1990), often with long periods between seasons, or perennials with only seasonal growth, such that there are long intervals in which there is no susceptible host tissue (e.g., because of natural leaf senescence) or the environment is unfavorable for disease development or crop growth. This article deals with epidemics of annual crops but has applicability to nonsystemic diseases of perennial crops with seasonal growth. The abrupt elimination of the annual-crop host at regular times (during harvesting), independent of disease status, and the subsequent introduction or reintroduction of the host at a later time (e.g., next season, when crops are planted), independent of the amount of pathogen inoculum in the soil or surrounding area, are complications not typically considered in theoretical epidemic models. A major challenge in plant protection is to develop the theoretical and experimental approaches for studying these so-called polyetic (multiple-season) epidemics (Zadoks 1999). In human host populations, forcing functions (such as cosine functions for the transmission rate parameter) are often used to represent temporal cycles of high and low disease transmission (Bolker and Grenfell 1993, Earn et al. 2000). This approach does not adequately represent the disappearance of the host nor the potential survival of the pathogen as a saprophyte or parasite of other plant species. The more formal single-season model is presented in Box 1 as equation 1. This is a generalization of the classic SEIR (susceptible, exposed, infectious, and recovered) model and is based on some of the models of Gilligan and colleagues for mixtures of primary and secondary infection (Gilligan and Kleczkowski 1997, Gilligan et al. 1997, Bailey and Gilligan 1999); the model also has similarities to those developed for animal epidemics in which the pathogen has a saprophytic stage (Godfray et al. 1999). For initial simplicity, growth or mortality of S during the growing season is not considered here. Depending on the values of the parameters of equation 1, pure primary-infection-only (i.e., “simple interest”) and pure secondary-infection-only (“compound interest”) epidemics can be obtained (Box 1). Moreover, most single-season epidemics of crops can be characterized through the model parameters. One composite parameter, βS0/γ, is especially useful in this regard; βS0/γ equals the within-season basic reproduction number (Diekmann et al. 1990) for secondary-infection-only epidemics. Both increasing transmission rate (β) and increasing length of the infectious period (1/γ) lead to increases in βS0/γ. The single-season model of equation 1 can now be expanded for multiple seasons. Crop harvest occurs at t = Tg. After this time, all plant abundances are set to 0. We assume that new inoculum, which may survive between growing seasons, is produced by diseased individuals. Although only the I individuals produce inoculum that can cause secondary infections during the within-season epidemic, disease in all states theoretically could produce inoculum for the next season. For instance, spores may be produced or released (or both) from diseased noninfectious roots as they decay in the soil or on the soil surface (Agrios 1997). Moreover, this new inoculum may be in the form of infected alternate perennial (weed) hosts. The number of spores (or amount of inoculum) produced per diseased individual at the end of the season is given by θI, θE, and θR for the plants in the infectious, latent, and removed states, respectively; total number of spores produced is then given by κI, κE, and κR for the three infection categories (see Box 1). Model terms for primary and secondary infection, latent and infectious periods within seasons, and inoculum decay within and between seasons are consistent with empirical data and modeling evidence (Zadoks 1961, Sumner et al. 1985, 1990, Campbell and Madden 1990, Hall and Phillips 1992, Jeger and van den Bosch 1994, Hall 1996, Bailey and Gilligan 1999); however, in no study have all these factors been simultaneously considered. Although the proportionality between disease in one season and the amount of overwintering inoculum is well accepted (Zadoks 1999), quantitative information about the relationship of disease at the end of a growing season to newly produced P is scant. It should be emphasized that the expression for Q is not dependent on the simple functions used in Box 1 for the κ values; other functions could be substituted when information becomes available. Our model is similar to that developed by Gubbins and Gilligan (1997) and Truscott and colleagues (1997), although we used a simpler equation for S (in the current work) to facilitate derivation of a persistence threshold. Although Q can indicate short-term behavior of the process (e.g., between the first and second seasons), it does not necessarily indicate long-term dynamics. To determine persistence formally, we assume that the epidemic in the first season starts from a small (infinitesimal) P0 so that the introduced inoculum or the inoculum produced by I individuals does not contact a diseased individual during the epidemic. This assumption is reasonable in practice, because it is unlikely that a large amount of inoculum, relative to the size of the crop, would be introduced accidentally or deliberately. With this assumption, there is in effect no limitation to the increase in diseased individuals, and the variable S is replaced by the constant S0 in equation 1. This results in the elimination of the equation for S. The equations can be solved analytically for E, I, R, and P. Results are shown as equation 2 in Box 2. The necessary condition for persistence (of the pathogen or disease) over multiple seasons is an R0 greater than or equal to 1. A key result is that even if a large amount of inoculum is introduced, so that disease dynamics can be accurately described only by the density-dependent model (equation 1), R0 as defined in equation 4 is still the correct predictor of persistence. A heuristic argument explains this conclusion. Suppose R0 (or Q0) is less than 1, and recall that Q0 is equal to or greater than Q (by definition); thus, Q also is less than 1 in this situation. P0 at the start of season 2 will be less than P0 at the start of season 1, even if a large amount of inoculum is introduced and all (or nearly all) plant individuals become diseased by the end of the season. P0 declines each season until eventually it is low enough for the density-independent model to hold (with the solution in equation 2). Then, P0 at the start of subsequent seasons is directly determined from P0(Q0)η, in which η is the season number beginning when density-independence holds. Now consider a situation in which a large amount of inoculum is introduced, Q is less than 1, but R0 is greater than 1. In this case, P0 initially declines for a number of seasons (because Q < 1) until inoculum is low enough that the density-independent model (equation 2) holds. However, the disease does not go extinct because—at low inoculum levels—each unit of inoculum produces more than one new unit of inoculum (because R0 [or Q0] > 1). To determine the conditions necessary for persistence or no persistence, one can solve equation 4 for the parameter values that give R0 = 1. This is demonstrated in Figure 3 for situations in which plant individuals in the I and R states contribute to inoculum production at the end of the season. Persistence occurs whenever the parameter values for a given disease lie above the appropriate curve. Although the basic reproduction number for continuous “season-less” crops (βS0/γ) must be greater than 1 for persistence with pure contagious (secondary-infection-only) epidemics, βS0/γ can be considerably less than 1 and the disease and pathogen will still persist over multiple seasons. This will happen if inoculum mortality (μb, μg) is low, the production of P from infected plant individuals (i.e., θs) is high, or, for diseases with both primary and secondary infections, the primary infection rate (υS0) is moderate to high. For instance, consider Figure 3c, which represents a disease with low inoculum mortality during and between seasons. When there are 10 P individuals (units of inoculum) produced per infectious and removed diseased plant at the end of the growing season (i.e., θ = 10), persistence will occur at a low primary infection rate of υS0 = 0.002 per day when βS0/γ is greater than 0.62. When υS0 is increased to 0.005 per day, persistence will occur with βS0/γ = 0 (i.e., no secondary infections during the season are required). At higher θ (e.g., θ = 50) for these same inoculum mortality conditions (Figure 3c), almost any positive value of primary infection rate and βS0/γ will result in persistence because so much inoculum is produced per infected plant individual. On the other hand, at a low θ value (e.g., θ = 1), persistence will still occur at βS0/γ < 1 if the primary infection rate is high enough (υS0 > 0.02 per day, a high value). Even for pure contagious (secondary-infection-only) epidemics, persistence can occur when βS0/γ < 1. With high inoculum mortality within and between seasons, as shown in Figure 3b, persistence can also occur at βS0 / γ < 1, but only if the per-unit production of inoculum (θ) and primary infection rate (υS0) are high. For example, at θ = 50, persistence occurs at υS0 = 0.01 per day (a high value) and βS0/γ > 0.74. These persistence situations with low βS0/γ represent crop diseases, typical of those caused by soil-borne pathogens, that manifest relatively little increase in the number of diseased individuals the first year after a pathogen is introduced and then a gradual increase in diseased individuals each year as inoculum builds up (Hall 1996); the same pattern of gradual increase for crops in P is initially βS0/γ may to be considerably above 1 for persistence (Figure especially if the primary infection rate (υS0) is low, production of inoculum from diseased individuals is low, mortality of inoculum is high, or within-season mortality of inoculum is high that little inoculum until the next for pure contagious epidemics, βS0/γ may also to be considerably above 1 for persistence if only a small number of plant individuals become infected per unit of inoculum Box 1). For instance, persistence will occur at θ = 1 and υS0 = only if βS0/γ is greater than (Figure With 10 times as much inoculum produced at the end of the season (i.e., θ = and other conditions persistence will occur if βS0/γ is more than For pure contagious epidemics, a value of βS0/γ greater than 1 will be for persistence if the number of new plant infections at the beginning of a season per unit of inoculum Box 1) is less than 0.01 and θ is These persistence situations with high βS0/γ would to many diseases with a increase in the number of infected individuals during the season but little inoculum survival the host (Zadoks period has no on persistence for a crop because all infected individuals eventually become infectious (in the but the latent period can have a large on persistence in a situation when = 0. This is because not all infected individuals will necessarily be infectious by the end of each season, and not all infected individuals will produce factors determine a pathogen introduced deliberately or accidentally will be a survive between seasons, and persist (Yang et al. 1991, Schaad et al. 1999). epidemiological theory can be used to predict invasion and persistence for situations in which there is no of disease development by or other condition Anderson and May 1990, Campbell and Madden 1990, Jeger and van den Bosch We have expanded on this theory by explicitly disease in annual crops over multiple seasons, and we have presented a to determine which of within-season and population will lead to persistence in annual This into the epidemiological for and crop diseases by to biological weapons it can the first in a or risk of pathogens (MacKenzie 1999, Schaad et al. 1999). In one could the of some pathogenic with the basic reproduction number in (Schaad et al. used to determine the most pathogens of one can use such as Figure 3 to determine persistence is for a given pathogen a of by model parameters. Figure 3 more than one set of pathogenic or disease can lead to persistence and high disease diseases, which have been considered and developed as (Whitby and Rogers 1997, Rogers et al. 1999), have high within-season basic reproduction number (βS0/γ) values to high disease in a season. a pathogen could have a major economic impact during the year of but overwintering survival may be very low (because of low or high to thus, this of introduced disease is unlikely to cause long-term economic pathogen inoculum is It should be emphasized that βS0/γ and other parameters (and are dependent on the environment Campbell and Madden 1990). for diseases with very high within-season of increase of may be low or very low during many other in R0 being less than 1. On the other hand, pathogens with low mortality in the of the or with a of alternate perennial could persist even when disease development within growing seasons is is the soil-borne which has been considered as a biological for the of et al. This species also has been extensively as a for and 1999). is a soil-borne pathogen that a plant and there is little if any secondary of disease between an increase in disease within a growing season is due to primary However, many species can survive in the soil between growing seasons, which could result in a high The introduction of such a pathogen may not cause large economic losses in a year a very large amount of inoculum has been introduced into a crop, in which efforts would have to be to the amount of inoculum and persistence. of a disease secondary infection during the growing season but with low mortality between seasons is or of caused by and It is now that to develop these pathogens as weapons (Whitby and Rogers 1997). plant pathogens may a of moderate βS0/γ, primary infection and in R0 greater than 1 if conditions are One is pathogen considered for et al. 2000), which is characterized in a number of by a moderate increase in disease within a growing season and in survival between seasons. The of the modeling approach in this article is that are available for most of the model parameters for many diseases being (and to if they are not the parameters can be estimated from other population such as the rate of increase for diseases (Campbell and Madden 1990, Madden et al. 2000). With these parameter R0 can be (equation and used to predict persistence. When persistence is > 1), the relationship between the of infected plants and can be very in predicting the of the disease When is to be high, disease can be developed by on the epidemic that determine R0 (e.g., primary and secondary infection inoculum However, much more parameter will be if about final epidemic outcomes are The modeling also that one in our of polyetic diseases (Zadoks the production of new overwintering inoculum from diseased individuals κ functions and θ is to provide of the θ terms or to that more to be considered. The model can be in for greater crop growth during the growing season and Gilligan can be for example, as well as dynamics, and of disease through Figure 1. of disease within-season dynamics of disease-free infected infectious and the production of inoculum or pathogen individuals and mortality of inoculum within and between seasons Figure 2. plant individuals of and inoculum of over 10 years for an annual crop with a growing season of growing season starts with a disease-free and crop abundance of S0 = 1, and disease and pathogen dynamics as in equation 1. P for season 1 equals 1. (a) rate of within-season disease increase (with a within-season basic reproduction number, βS0 / of but with a high inoculum decay rate between seasons = per The basic reproduction number, equals (equation (b) rate of within-season disease increase (with βS0 / γ = but with a low decay rate between seasons per so that R0 equals The primary infection within-season inoculum mortality mean latent mean infectious and per-unit production of inoculum are the same for both Figure values of the plant epidemic model that produce a basic reproduction number equation of 1. For all the growing season is mean latent period is the per-unit production of inoculum is the same for infectious and removed diseased individuals as and infected plant individuals not produce new and pathogen persistence occur when the primary infection and the within-season basic reproduction number, βS0 / are above the for the θ and other parameters given above or within the The on the and to values of the within-season inoculum mortality rate the and to values of the mortality rate Figure The value of the of infected plant individuals at the end of each season the epidemic has into a within-season on the of density-dependent equation 1, in to (a) the basic reproduction number equation or to (b) the of obtained for a of parameter with a growing season of in all of the growing season may the but not the basic relationship