Blood Feeding & Transmission
Parasite Transmission through Blood Feeding
Topics: Parasite transmission from humans to mosquitoes, and from mosquitoes to humans. The human biting rate (HBR), the sporozoite rate (SR), and the entomological inoculation rate (EIR). The average intensity of malaria transmission in relation to mosquito and human population population density.
Blood Feeding
An important concept that we must understand so we can describe it with mathematical formulas is parasite transmission among populations of humans \((H)\) and mosquitoes \((M)\) that is a consequence of blood feeding by mosquitoes.
The parasite life-cycle requires two blood feeding events: transmission from humans to mosquitoes in the bloodmeal \((H \rightarrow M)\); and transmission from mosquitoes to humans in the bite \((M \rightarrow H)\):
\(H \rightarrow M\) :: A mosquito gets infected after consuming human blood that has both macrogametocytes (female) and microgametocytes (male). In the mosquito midgut, one of each (i.e. one micro- and one macro-gametocyte) mates to form a gamete. After meisis, and some early parasite development, an ookinete forms and embeds in the mosquito midgut, where it forms an oocyst. At this point, we would call the mosquito infected.
\(M \rightarrow H\) :: A human can become infected after getting bitten by a mosquito that has sporozoites in its salivary glands. The sporozoites enter the bite wound in saliva and then, if they are not all consumed when the mosquito has sucked some blood (and saliva), some sporozoites enter the blood and infect cells in the liver. At this point, we would say that a human has been infected, but it is only around 7 days later, when parasites emerge from the liver and begin to replicate asexually in blood. A few days later, we might detect parasites and notice the symptoms of malaria.
Two distinct blood feeding events (bloodmeal and bite) are required for the parasite to complete one generation. We can count a generation either from a human through a mosquito and back to other humans; or from a mosquito through a human and back to other mosquitoes.
Parasite Generations
If we followed a parasite over time and across generations, we would trace out the full parasite life-cycle. What is, perhaps, most relevant for understanding parasite generations and malaria in populations is that the events in a parasite life-cycle require time for parasite development:
Parasites replicate in the oocyst and then they form sporozoites that migrate through the hoemocel of the mosquito into the salivary glands. This process of parasite development takes several days. The time elapsed from the infecting blood meal to the point when sporozoites can be detected in the mosquito salivary glands is called the extrinsic incubation period (EIP).1 A large fraction of infected mosquitoes will die before they become infecious.
We have already described the parasite’s brief liver phase, but parasites in blood are not ready to infect mosquitoes immediately after emergence. Instead, two things must happen: parasites must form gametocytes and mature; and mature gametocytes must reach high enough concentrations to infect a mosquito. During the asexual phase in blood, some of the parasites that had been reproducing asexually make a commitment to becoming gametocytes. At that point, gametocyte maturation process takes 8-12 more days, so the earliest a mature gametocyte could appear is around 15 days after the infecting bite. The densities of mature gametocytes increase rapicly, but humans are not likely to infect a mosquito for 20-30 days after the infecting bite.
The shortest time required for a parasite to complete one generation is thus approximately one month. These details about the temporal dispersion of a parasite generation will become important later.
Blood Feeding Rates & Habits
The number of human blood meals taken by a mosquito each day is constrained by mosquito biology. Mosquitoes blood feed on humans and other vertebrate animals, and then they turn that blood into eggs, and they they lay those eggs in aquatic habitats. After blood feeding, mosquitoes typically rest, take some time to concentrate the blood meal and shed excess water. Some time is required to lay eggs. After this, some mosquitoes might seek a sugar meal to top up the energy reserves. After searching for water and sugar, it might take some time to search for a human or other blood host to blood feed again. There are some interesting and perhaps important exceptions – a mosquito could get interrupted after biting or take a partial blood meal and feed again – but from a basic description of mosquito blood feeding and egg laying behaviors, we can quantify the average interval between blood meals.
Given the biological constraints on a mosquito, we can describe two important aspects of blood feeding: the overall mosquito blood feeding rates and their blood feeding habits:
\(f\) – the blood feeding rate is the expected number of bloodmeals that a mosquito will in a day; mosquitoes typically blood feed once every few days.
\(q\) – the human fraction is the expected fraction of blood meals taken on a human: it is human blood meals as a proportion of total blood meals.
The human fraction is a quantitative way of describing anthropophagy, or blood feeding on humans. This is distinct from anthropophily, a preference for human blood.
We will come back to blood feeding again, when we develop a framework to understand how these two parameters arise in context where mosquitoes search for blood hosts, and respond to the availability of resources.
Transmission Dynamics
The biological constraints imposed by blood feeding change dictate a set of mathematical rules for transmission that are different from other diseases: mosquito-transmitted pathogens don’t work the same way as directly transmitted pathogens. Some analysts who come to malaria have had some experience modeling measles, flu, SARS, or some other directly transmitted pathogens, where viral particles are shed into the air and breathed in by others. Mass shedding creates the opportunity to infect large numbers of others, so transmission is mainly limited by opportunities for contact. As an example, if a single human infected with influenza went to a sporting event, shedding billions of particles, the number of people who might get infected would depend mainly on the number of susceptible people passing through their cloud of of viral particles.
With malaria, and with other mosquito-transmitted pathogens, transmission only happens through blood feeding. The number of blood feeding events (bites or bloodmeals) is limited by the number of mosquitoes and the blood feeding rate. The total number of mosquito blood feeding events in an area, per day – a single instance counted from when a mosquito probiscus has penetrated human dermis – is limited by the blood feeding rate per mosquito and the number of vector mosquitoes, \(M\). If we define an area, the number of human blood meals taken by mosquitoes in a day is \(fqM.\) If there are \(H\) humans in that area, then the average Human Biting Rate (HBR), the expected number of bites by vector mosquitoes, per human, per day is, \[\mbox{HBR} = \frac{fqM}H.\] This formula says that the overall intensity of blood feeding, per human, is linearly proportional to the number of mosquitoes, but it is inversely proportional to the number of humans.
The rate of exposure, called the Entomological Inoculation Rate (EIR), is defined as the number of bites by infectious mosquitoes, per human per day. If we let \(Z\) denote the number of infectious mosquitoes, then \[\mbox{EIR} = \frac{fqZ}H.\] Since mosquitoes are presumed to be infectious if they have sporozoites in their salivary glands, we can define the sporozoite rate 2 (SR): \[\mbox{SR} = z = \frac{Z}M.\]
So now we can write a general formula that defines the EIR as a field metric and as a quantity that we will come back to in our models: \[\mbox{EIR} = \mbox{HBR} \times \mbox{SR} = mfqz = fq\frac{Z}{H}\]
Mosquito Density
Since the vector mosquitoes we are interested in blood feed on humans, it stands to reason that mosquito densities should be related to human population densities. While humans are certainly one resource mosquitoes need, we are not the only one.
Adult mosquitoes lay eggs in aquatic habitats, where the eggs hatch into larvae. The water bodies are generically called aquatic habitats. In aquatic habitats, larvae compete for resources and molt into 4 distinct larval instars before pupating. There are good reasons to believe that competition and other biotic factors play a role in regulating mosquitoes in these aquatic habitats. So while humans are an important resource for mosquitoes, the amount of available aquatic habitat is probably the most important limiting factor. These are topics we take up in Mosquito Ecology
Footnotes
We will stick to the traditional terms, but we wish to draw attention the fact that in modern terns, the EIP is neither extrinsic, nor is it an incubation period. Using modern terms, the time elapsed before becoming infectious is called a latent period. As we have implied in our description, the mosquito would be called the definitive host for malaria parasites, because it is the organism where parasites complete gametocytogenesis.↩︎
Once again, we are keeping with traditional terms. This would not be called a rate if it were named today. It is a measure of prevalence.↩︎