Vectorbased diseases malaria

Diseases that are transmitted from one host to another via vectors rather than direct contact are common and important. For example (Spielman and D'Antonio 2001), mosquitoes transmit malaria (Anopheles spp.), dengue and yellow fever (Aedes spp.), West Nile Virus and filariasis, the worm that causes elephantitis (Culex spp.) (Figure 5.10). In this section, we will focus on malaria, which continues to be a deadly disease, killing more than one million people per year and being widespread and endemic in the tropics. The history of the study of malaria is itself an interesting topic and the book by Spielman and D'Antonio (2001) is a good place to start reading the history; Bynum (2002) gives a two page summary, from the perspective of Ronald Ross. From our perspective, some of the highlights of that history include the following.

• 1600s: Quinine derived from tree bark in Peru is used to treat the malarial fever.

• 1875: Patrick Manson uses a compound microscope and discovers the organism responsible for elephantitis.

• 1880: Pasteur develops the germ theory of disease.

• 1880: Charles Levaran is the first to see the malarial parasite in the blood.

• 1893: Neocide (DDT) is invented by Paul Mueller as a moth killer.

• 1890s-1910s: A world-wide competition for understanding the malarial cycle involves Ronald Ross (UK), Amico Bignami (Italy), Giovanni Grassi (Italy), Theobald Smith (US), W. G. MacCallum (Canada). The win is usually attributed to Ross, who also develops a mathematical model for the malarial cycle. In 1911 Ross writes the second edition of The Prevention of Malaria.

• 1939-45: During World War II, atabrine, a synthetic quinine, is developed, as is chloroquinine; DDT is used as a delouser in prisoner of war camps.

• 1946-1960s: Attempts are made to eradicate malaria and they fail to do so; resistance to DDT develops.

• 1950s: G. MacDonald publishes his model of malaria and studies the implications of this model. In 1957 he writes The Epidemiology and Control of Malaria.

• 1960: The first evidence of resistance of the malaria parasite (Plasmodium spp.) to chloroquinine is discovered.

• 1962: Rachel Carson's Silent Spring is published. John McNeil (2000) has called Silent Spring ''the most important book published by an American.'' If you have not read it, stop reading this book now, find a copy and read it.

Figure 5.10. (a) The malarial mosquito Anopheles freeborni (from the Public Health Image Library (PHIL) found at http://phil.cdc.gov/phil/default.asp thanks to Dr. James Gathany). (b) Egg rafts of the carrier of avian malaria Culex laticinctus, and (c) Culex attacking a host (both compliments of Dr. Leon Blaustein, Haifa University). (d) Ookinete of the human malaria parasite Plasmodium falciparum (top-right corner) within the basal region of the midgut wall of the mosquito vector Anopheles stephensi. The ookinete probably resides within the intercellular space between adjacent midgut cells, after having passed intracellularly through the midgut epithelial cell that exhibits abnormal dark staining (compliments of Dr. Luke Baton and Dr. Lisa Ranford-Cartwright, University of Glasgow).

Figure 5.10. (a) The malarial mosquito Anopheles freeborni (from the Public Health Image Library (PHIL) found at http://phil.cdc.gov/phil/default.asp thanks to Dr. James Gathany). (b) Egg rafts of the carrier of avian malaria Culex laticinctus, and (c) Culex attacking a host (both compliments of Dr. Leon Blaustein, Haifa University). (d) Ookinete of the human malaria parasite Plasmodium falciparum (top-right corner) within the basal region of the midgut wall of the mosquito vector Anopheles stephensi. The ookinete probably resides within the intercellular space between adjacent midgut cells, after having passed intracellularly through the midgut epithelial cell that exhibits abnormal dark staining (compliments of Dr. Luke Baton and Dr. Lisa Ranford-Cartwright, University of Glasgow).

• 2000-2010: The World Health Organization (WHO) embarks on a program called Roll Back Malaria, with the goal of reducing world-wide deaths by 50%.

Malaria is caused by amoeboid parasites Plasmodium; currently there are four main species that cause human malaria (P. falciparum,

P. malariae, P. ovale, P. vivax). The parasite itself has a complex life cycle and has been divided into more than ten separate steps (Oaks et al. 1991). For our purposes, the malarial cycle might be described as follows.

• An infected female mosquito seeks a blood meal so that she can make eggs. The sporozite form of the parasite migrates to the salivary glands of the mosquito.

• After entering a human host during a biting episode, the sporozites invade the liver cells and over the next 5-15 days, multiply into a new form (called merozites) which are released and invade red blood cells. The merozites reproduce within the red blood cell, ultimately rupturing it (with associated symptoms of fever and clinical indications of malaria).

• Some of the merozites differentiate into male and female sexual forms (game-tocytes). These sexual forms are ingested by a different (potentially uninfected) mosquito during her blood meal. Once inside the mosquito, the gametes fuse to form a zygote, which migrates to the stomach of the mosquito and ultimately becomes an oocyst. Over the next week or so, the oocyst grows in the mosquito stomach, ultimately rupturing and releasing of the order of 10000 sporozites which migrate to the salivary glands. And so the process goes.

There are more than 2500 species of mosquito in the world, but only the genus Anopheles transmits malaria; there are about 60 species in this genus. The mosquito life cycle consists of egg, larval, pupal and adult stages. Females require a blood meal for reproduction and deposit 200-1000 eggs in three or more batches, typically into relatively clean and still water. The development time from egg to adult is 7-20 days, depending upon species and environmental conditions. Adult survival is typically of the order of a month or so (especially under good conditions of high humidity and moderate temperature). The adults seek hosts via chemical cues that include plumes of carbon dioxide, body odors and warmth (Oaks et al. 1991).

There exists in the literature what one might call the "standard vector model'' and we shall now derive it, using mosquitoes and humans as the motivation, but keeping in mind that these ideas are widely applicable. The key variables are the total population of humans and mosquitoes, HT and MT respectively, which are assumed to be approximately constant, and the population of infected humans and mosquitoes, H and M respectively. The malarial cycle is characterized by the following parameters.

a = Biting rate of mosquitoes (bites/time).

b = Fraction of bites by infectious mosquitoes on uninfected humans that lead to infections in humans.

c = Fraction of bites by uninfected mosquitoes on infected humans that lead to parasites in the mosquito. r = Recovery rate of infected humans (rate at which the parasite is cleared). p = Mosquito death rate.

Examples of clearance rates of parasites are found in Anderson and May (1991; figures 14.2 and 14.3). To begin, we compute the basic reproductive rate of the disease. Imagine that one human becomes infected with the parasite. This individual is infectious for an interval that is roughly 1/r. This infected human will thus be bitten a/r times andif we assume that the mosquitoes are uniformly distributed across hosts and that a mosquito only bites each human once, then the number of mosquitoes infected from biting this one infected human is ac(MT/HT)(1/r). Each infected mosquito will make approximately ab(1/p) infectious bites. Combining these, we conclude that the number of new cases is

The last re-arrangement of terms in Eq. (5.29) makes the dimensionless combinations of parameters clear. In the mosquito literature, there is a tradition of using Z0 for the basic reproductive rate. Perhaps the most important conclusion from this calculation is that the biting rate enters as a square, while all other parameters enter linearly. Thus, in general a given percentage reduction in the biting rate (e.g. by bed nets or by insect repellent) will have a much greater effect on the basic reproductive rate of the disease than a similar reduction in any of the other parameters. This was one of Ross's arguments for mosquito control as a means of malaria control.

We now construct the dynamics of infection. We begin with infected humans, H(t), who come from interactions between infected mosquitoes, M(t), and uninfected humans, HT — H(t). Assuming that transmission is characterized by mass action, thus depending upon the number of mosquitoes infected per human and the number of uninfected humans, and taking into account the clearance of parasites, we conclude that

As in the computation of the basic reproductive rate, we have distributed infected mosquitoes across the human population. Mosquitoes become infected in a similar manner: transmission between infected humans and uninfected mosquitoes. The dynamics of infected mosquitoes become

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    What do prisons use as a delouser?
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