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Toxoplasmosis is a parasitic infection caused by the protozoan Toxoplasma gondii. Humans can become infected by ingestion of raw or undercooked meat that contains tissue oocysts (the reproductive cell), or by direct contamination from the environment contaminated by infected cat feces. Although toxoplasmosis is most often asymptomatic in humans, it can cause serious illness in immune-compromised individuals and in fetuses. At this time, there is no cure for the disease; prevention is the only method of control. This model examines the principal factors that influence the spread of the disease from animals to humans on a case study of 43 Illinois swine farms. Most of the data for this model were obtained from2,3, and4. Some of the references are given in the model variable icons. The main questions we wish to answer with this model are: How is the prevalence of Toxoplasma gondii in people on swine farms in Illinois affected by exposure to cats, ingestion of infected food, and the handling of dirt? Which one of these factors affects the prevalence most? How would the prevalence be affected if we vaccinated the cats, and which rate would be optimal? [ABSTRACT FROM AUTHOR]

This chapter expands and refines some earlier models, which included life stages of insects, by specifically distinguishing two cohorts of a population infected with a disease. The two populations modeled here are insects that suffer from a disease that increases mortality for the infected nymphs and adults and also decreases their egg-laying rate. Unlike the previous chapters, we assume two populations of insects living in two fields. One of the fields has generally better living conditions than the other, although a current year΄s carrying capacities are randomly generated and there is some overlap in the ranges within which carrying capacities fluctuate. [ABSTRACT FROM AUTHOR]

If a large number of real systems exhibit dynamics that bear the potential for chaos, why do we not see more chaos in real-world processes? Fortunately, the domains over which stability of the system occurs can be relatively large. But once in a while, systems may move ˵toward the edge of stability″ and little nudges to the system may move it from stability to instability–that is, into a catastrophe. Subsequently, reorganization of system components may occur to bring the system back into a stable domain–a kind of evolutionary process. This stable domain, however, may not be the same as the one prior to the disturbance. The system undergoes a catastrophic event in the sense that it is moved from an initial state of stability through a dramatic phase of reorganization and back to some degree of stability. Examples for such catastrophic events include landslides, avalanches, earthquakes, and pest outbreaks in ecosystems. In each case, small changes in the system occur that individually may not be critical to the system΄s behavior. Collectively, however, they lead to the evolution of the system toward a critical state. This is apparent, for example, in the case of avalanches. Each individual snowflake potentially adds to the instability of the system. When a critical point is reached, the next snowflake may trigger an avalanche that affects a large part of the system. Temporary stability is quickly reached if the avalanche is not too dramatic. Even if not of a large scale, the avalanche adds to the ˵stress″ of the system downhill, making it more susceptible to further avalanches as more snow falls at those regions or as additional small avalanches are received from higher on the hill. Ultimately, a large-scale, catastrophic event may occur, which affects the entire system, not just individual regions. The system components re-group and finally enter a phase of new, temporary stability. [ABSTRACT FROM AUTHOR]

Before the advent of modern computer technology and software, many modeling efforts and scientific experiments were designed for linear, often static systems, which had the advantage of being analytically solvable. The ways of thinking about system behavior and the tools applied to describe that behavior was rooted deeply in classical mechanics. This science was used to describe the behavior of whole classes of moving objects, such as pendulums, falling rocks, or projectiles. The scientific paradigms associated with classical mechanics were not only applied in the realm of the natural sciences but increasingly influenced models of economic and ecological systems as well. The strength of these paradigms lies in their view of systems as predictable, welldescribed entities that can be analyzed with available mathematical tools. Students were told that nonlinear systems are generally unsolvable and that such systems are exceptions. The first of these statements is true; nonlinear systems, some of which we modeled in the previous chapters, generally do not have an explicit mathematical solution. However, the second statement, that nonlinear systems are exceptions, is false. Rather, many real systems are governed by nonlinearities. These systems frequently exhibit characteristics that were previously unanticipated or misidentified. The emergence of chaos theory made us aware of the importance of nonlinearities, a lack of predictability that is inherent in many of these nonlinear systems, the sensitivity of model results to small changes in initial conditions, and therefore, the need for increased computer modeling efforts. Today, chaos theory begins to influence thinking in modern natural sciences as well as in the social sciences. In the following sections of this chapter, we develop models with potentially chaotic behavior first in the context of the spread of a disease–akin to the simple models in Chapter 2–and then in the context of insect dynamics and associated host– parasitoid interactions, which we touch on throughout the book. [ABSTRACT FROM AUTHOR]

West Nile virus (WNV) is an arthropod borne, or arboviral, disease historically endemic to Africa. In Africa, the disease circulates between populations of wild birds and mosquitoes, but only occasionally results in significant disease outbreaks in wildlife1. After emerging in North America in 1999, however, WNV spread rapidly through avian communities, causing unexpected mortality in many bird species and encephalitis epidemics in secondary hosts, such as horses and humans. WNV is one of a number of related flaviviral encephalitides, including eastern equine encephalitis, Japanese encephalitis, and La Cross encephalitis. These diseases are all transmitted among hosts by mosquitoes and can result in symptoms ranging from mild malaise to severe neurological disease and death. In this chapter we build from a simple, population-dynamic SIR model of a contagious disease to an indirectly transmitted arboviral disease model with explicit population and seasonal dynamics. We use these models to qualitatively explore how host and vector natural history and population dynamics might change predictions as to how the disease outbreak will behave over time. [ABSTRACT FROM AUTHOR]

Throughout this book we have hinted at–or explicitly modeled–strategies that interfere with the dynamics of pests and diseases, such as using repellents in the malaria model or vaccination in the case of chicken pox. In this chapter, we focus on such interferences and concentrate on biological methods to control pests. The subsequent chapter then explores the effects of disease resistance. [ABSTRACT FROM AUTHOR]

The zebra mussel (Dreissena polymorpha) is a small bivalve mollusk native to Europe. The mussel was first observed in North American lakes only recently. Initial colonization may have occurred in 1986, probably from larvae discharged in ballast water. The zebra mussel is a potentially serious pest. In high densities, it presents major problems for both human-made structures and for the ecology of infested bodies of water. One of the most harmful impacts is the colonization of intake cribs and pipes serving water treatment plants, power generating stations, and industries. Attracted to swift-moving water carrying large amounts of nutrients, mussels quickly colonize and block these intake pipes. As an efficient feeder, the zebra mussel is capable of removing large amounts of seston from the water. A benthic (bottom dwelling) organism, the zebra mussel effectively removes nutrients from the water column and deposits them on the bottom of the lake, river, or estuary in which it lives. In addition to diverting primary productivity from the plankton to the benthos, zebra mussels may also cover substrates used by other organisms and foul sedentary benthic organisms. [ABSTRACT FROM AUTHOR]

Chicken pox, a microparasitic infection caused by the varicella zoster virus, is an example of a highly infectious childhood disease. This virus can be spread either through direct contact with infected individuals or through the air. After exposure to the virus, the incubation period before an individual becomes contagious is approximately seven days. Individuals are contagious for about seven days during which symptoms including fever and blisters appear, and then remain sick for an additional fourteen days. Once an individual recovers, he or she develops a natural immunity and is unlikely to get the disease again. However, the virus remains in the body and later in life, it manifests itself in the form of shingles in about 15 percent of the population that contracted chicken pox. Shingles has symptoms that are similar to chicken pox but strikes mostly individuals over the age of 50 that are fatigued or under stress. It takes approximately 10 days to recover from shingles and during this time susceptible individuals can contract chicken pox from those suffering from shingles. New vaccines are becoming available to immunize people against chicken pox. The target population for immunization typically is children, because they comprise the highest infectious class. Immunizing children would help to reduce occurrence of chicken pox. However, no vaccination program can reliably cover 100 percent of a population. Consequently, as childhood vaccination takes place, fewer cases of chicken pox among children occur but the age of first infection increases. Since older individuals have more difficulty dealing with chicken pox than young individuals, vaccination programs may shift the burden from the young to the old. [ABSTRACT FROM AUTHOR]

Over the past 20 years since Lyme disease was first diagnosed, it has been identified as the most common vector-borne disease in the United States. The repopulation of white-tailed deer in the United States of America has been associated with the emergence of this disease. The tick vector, Ixodes scapularis, harbors Borrelia burgdorferi (B.b.), the organism responsible for Lyme disease2. The larval and nymphal stages feed on intermediate hosts, which are mostly small mammals and birds. The adult tick prefers to feed on deer, but will also feed on dogs and people. The main intermediate host in the northeast United States is the white-footed mouse. Mice and chipmunks may serve as reservoirs for B.b. in nature since they maintain active infections for at least 3 to 4 months. In the Midwest, however, it has been determined that the eastern chipmunk may be equally important as an intermediate host. The ticks appear to follow the migration of deer but deer may be simply an amplification host; they are able to clear infection from B.b. within a few days. [ABSTRACT FROM AUTHOR]

Chagas disease, also called American Trypanosomiasis, is one of the most prominent vector-borne diseases in Latin America. It is caused by the protozoan parasite, Trypanosoma cruzi, and transmitted by blood-feeding triatomine bugs. Infection occurs not by the biting of the bugs, but by infiltration of the feces of infected bugs during blood feeding. In rural areas of Argentina, for example, most people acquire infection in their homes because the cracks in the walls of their houses and the thatched roofs under which people live tend to be shelters for triatomine bugs. Furthermore, domestic and peridomestic animals, such as dogs and chickens, often occupy people΄s bedrooms, thus providing sufficient blood sources for the bugs. Human-to-human transmission is generally impossible, but a few infants are infected by their mothers, who already have Chagas disease, and in rare cases people can contract Chagas disease through blood transfusions. Because of the central role of animal-to-human transmission, more focus on Trypanosomiasis infestans as a main vector of the Chagas disease in domestic housing of Argentina1 is expected, even though many species of triatomine bugs transmit Trypanosomiasis cruzi throughout the geographic region. Currently, neither vaccine nor prophylaxis is available.An effective drug treatment is used for humans only in the acute and early chronic phase of infection. People cannot develop immunity for Chagas disease even after recovering from the infection. Possible control measures for Chagas disease are 1) improving housing, 2) annual spraying of insecticides and killing of triatomine bugs, 3) providing early prevention for infants born to infected mothers through congenital surveillance and treatment of infected infants, 4) excluding reservoir animals from human housing, and 5) blood screening. [ABSTRACT FROM AUTHOR]

A virus transmitted between hosts, most commonly by mosquitoes and ticks, causes encephalitis. The disease is kept extant by a complicated transmission process between humans and a vertebrate host such as a horse. Humans and domestic animals are terminal hosts. They suffer from the disease but do not spread the disease themselves. Several paths of transmission and several variants of the virus are known. Most often, the transmitting vector (mosquito or tick, for example) will pass the virus to his or her own offspring. Four distinct types of mosquito-transmitted encephalitis are found in the United States: western equine, eastern equine, St. Louis, and La Crosse. The time period for appearance of the disease is from June through September and even into winter in the warm parts of the country. The virus causes flu-like symptoms that are seldom fatal. Currently, antibiotics and vaccines approved by the Food and Drug Administration are ineffective. The disease is best prevented in humans by the use of specific pesticides and protective clothing and by avoiding the transmitting insects. Detailed data for this serious public health problem have been collected in many parts of the country. Yet, relatively few models of the disease have been made. We offer one such model of St. Louis encephalitis in Illinois. Models of this disease are useful as public health instruments as they enable better prediction of the conditions for its appearance, and because they can be used to evaluate the effectiveness of intervention programs. The combination of good models, an aware public, and an alert and efficient public health service can combine to effectively control this disease. [ABSTRACT FROM AUTHOR]

Malaria is one of the most severe human diseases, causing more than 300–500 million cases today1, leading to an estimated 2.7 million deaths worldwide with 80–90% of those occurring in the section of Africa below the Sahara Desert. Children ages one to four are most vulnerable to malaria due to their immature immune systems. Malaria is caused by a parasite transmitted to humans or animals by the Anopheles mosquito. The human parasite, Plasmodium falciparum, digests the hemoglobin found in red blood cells (RBCs) and breaks down the adhesive properties of the cells. Therefore the RBCs may become stuck to the walls of capillaries. When this occurs in the cerebral section of the brain, cerebral malaria develops, and blood clots in the brain occlude the vessels. Symptoms of malaria increase in severity each time an RBC bursts and releases more parasites. These symptoms can include high fever, chills, and uncontrollable shaking/shivering, also called rigors. Severe headache, vomiting, muscle pain, and extreme tiredness may accompany these symptoms as well. To combat the disease, many countries use an insecticide called DDT to control mosquito populations. Different medications have also been developed to treat and prevent malaria. These include chloroquine, doxycycline, and mefloquine. Several variables are implicated in the epidemiology of this disease. In this chapter we develop a simplified model to investigate the dynamics of the spread of malaria in a closed ideal region without human immigration. We further assume that humans are the most important hosts and disregard other possible hosts aside from the mosquitoes, which pick up the malaria parasites when they feed on the blood of an infected human. Upon receipt of malaria parasites (Plasmodium sp.), the parasites reproduce in the gut of mosquitoes. Subsequently, malaria parasites are returned through the mosquitoes΄ salivary glands to humans as the mosquitoes feed on red blood cells. [ABSTRACT FROM AUTHOR]

In this chapter we develop three different models of insect dynamics. From the perspective of ˵dynamic modeling of pestilence,″ insects surely need special attention–they are the carriers of many of the viruses that affect the health of humans and other animals, and they cause billions of dollars of damage to food supplies around the world every year. We try to control their population levels, having long ago realized they multiply and evolve too fast for elimination. Insects are among the major vectors of disease. They provide an excellent way to understand the dynamic modeling of a complicated disease vector composed of different age classes. From a modeling perspective, insect dynamics can be used to effectively illustrate a set of techniques and skills that will prove important for gaining a deeper understanding of (a) the challenges of matching laboratory and field experiments to models(b) the underlying mechanisms by which living systems evolved and adjust to their external environment(c) the distinct roles that different life stages or age cohorts may play in the transmission of, or infection with a disease The following three sections of this chapter respectively address these issues. Later chapters either explicitly or implicitly make use of the insights gained here. [ABSTRACT FROM AUTHOR]

In this chapter we follow up on our discussion from Chapter 1 and model the spread of a disease through a population, gradually adding new features. Epidemics, such as the one modeled here, are of great concern to human societies. The complex interrelationships of biological, social, economic and geographic relationships that drive or constrain an epidemic make dynamic models an invaluable tool for the analysis of particular diseases. The model developed here is fairly idealized but can be applied easily to real populations affected by a disease. Assume that an initial population of 1,000,000 (per 100 square miles) is not immune to a contagious disease. The rate at which they become sick is assumed to be a function of the product of the nonimmune population times the contagious plus sick population. This equation for contagion is the simplest form that meets the obvious requirements that the contagion rate must be zero if either the immune or the contagious populations are zero. The contagious population is assumed to become the sick population for a week and then, with a survival rate of 0.9, the survivors join the immune population. The nonimmune population is augmented with a constant birth rate of 5000/week. The people in this model do not die of other causes. [ABSTRACT FROM AUTHOR]

Few tasks are nobler than those that improve the length and quality of life of humans and their fellow species. And few tasks are more difficult to accomplish. To be successful, we must assess the vulnerabilities of individuals to attacks on their health and well-being, we must understand the interactions of individuals with each other and their environment, and we must anticipate the likely consequences of all these factors in an ever-changing world–individual vulnerabilities change, new diseases and pests emerge, old ones reappear, new means are developed to detect and combat adverse influences on health and well-being, and new standards for health and quality of life are applied. There are many drivers behind the spread of diseases and pests. Climate change may create new temperature and precipitation regimes conducive to diseases and pests that would otherwise be irrelevant for particular locations. West Nile fever, malaria and encephalitis, for example, are increasingly of concern to public health officials. Other drivers are related to our use of technology in a globalizing world. For example, ballast water used in ships can carry with it organisms and spread them to ever more far-flung places. Increased travel of people around the globe can promote dispersal of viruses, bacteria, fungi, and other ˵agents″ that affect the health and well-being of species and ecosystems. [ABSTRACT FROM AUTHOR]

Being able to better understand how diseases and pests are propagated and how they may be contained requires knowledge of the many factors that influence their success or failure. The combination of chance events, time delays, and nonlinearities in complex social and environmental settings make predicting spread of diseases and pests a daunting task. Yet, some method for sorting through the myriad of factors and influences and for anticipating future dynamics is required to meet dual goals of improving the state of human welfare and maintaining healthy ecosystems. In this book we provided one particular, and very powerful, way of looking at the world. We concentrated on the forces that underlie different dynamic systems. Others, with different educational or cultural backgrounds, may choose a different approach and may develop different models. The potential diversity of perspectives and approaches in modeling is a challenge for all of us and should be perceived as an opportunity to engage in cross-disciplinary and cross-cultural dialogue about the world in which we live. [ABSTRACT FROM AUTHOR]