A tendency of mosquitoes to prefer infected humans affects how fast malaria spreads in a community, says S.Ananthanarayanan.

This unexpected bias of mosquitoes, which has been recently discovered, is one of the factors that have been considered in developing a mathematical formula of how an outbreak of malaria may progress.

Xiunan Wang and Xiao-Qiang Zhao, of the Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Canada, publish in the journal of the Society for Industrial and Applied Mathematics, their study of malaria transmission dynamics, or the factors that influence how the numbers of infected persons rise or fall and how mosquitoes flourish or flounder.

“Mathematical models provide powerful tools for explaining and predicting malaria transmission trend, and also for quantifying the effectiveness of different intervention and eradication strategies in malaria endemic regions,” the authors say in the paper. As the data of instances of infection is often inadequate, statistical methods need to be employed both to devise and to evaluate strategies for the prevention and then the management of malaria. In the context, it is useful to have an understanding of how the malaria pathogen behaves and adapts in different conditions that we are able to monitor.

We can see that whether instances of malaria in a community would persist depends how soon mosquitoes may pick up the pathogen from infected persons, how soon they are ready to infect others and then also on how fast mosquitoes breed and on how likely they are to bite infected persons, to acquire the pathogen and then to bite susceptible persons.

The model that Wang and Zhao have created takes into account three factors that affect the infection cycle: the first is the climate, which affects the breeding of mosquitoes. The second is the time it takes for the malaria parasite, once it has entered the mosquito’s body, to develop into the form for the mosquito to be able to infect a person. And the third is the recently discovered feature, that the mosquito, in taking a blood meal, appears to select infected persons in place of going for all persons with equal likelihood.

The climate factor, and particularly the temperature, is found to be important, as the breeding time for mosquitoes reduces from 65 days to 7.3 days if the ambient temperature rises from 12°C to 31°C, the paper says. The second limiting factor is the time it takes for the malaria parasite to develop within the mosquito and migrate to the salivary glands, from which it can enter the bloodstream of a person or animal that the mosquito feeds upon. This time, a delay, after the mosquito picks up the infection, is called the Extrinsic Incubation Period and can range from 10 to 30 days. As the lifetime of a mosquito can be from 3 to 100 days, some of the mosquitoes may not live long enough to be infective, while those that live longer than the incubation period would be infective for the rest of their days.

The third factor, called vector-bias, or the selective behaviour of the mosquito, which is the agent that carries the infective material, has been observed and studied by a number of researchers since the 1980s. Experiments showed that mosquitoes preferred malaria infected hosts at the stages of attraction and penetration, of probing and location of blood, and again of the taking of blood. This was the case with experimental mice and hens infected with malaria and the attraction for infected targets was there even when the mosquitoes were prevented from performing the actual bite. A more recent study, in 2005, was with three groups of children in western Kenya, where one group was uninfected, the second group was infected with the non-infective stage of falciparum malaria and the third group with the active phase of the infection. The third group was found to attract twice as many mosquito bites as the first two groups. A follow-up trial was then conducted after the children were cleared of the infection by treatment, and it was found that mosquitoes now showed no preference, including for the group that had earlier harboured the active infection.

This bias of mosquitoes towards malaria infected hosts appears to be some effect that the malaria parasite has evolved to have upon hosts, to act as a signal to attract mosquitoes. This would be an adaptation by which the parasite promotes its own transmission to new hosts and hence its perpetuation. Here, it should be mentioned that it is the female mosquito, who needs protein for her reproductive role, that feeds on blood meals from people and animals. The male mosquito, in contrast, is content with nectar from plants. While the female mosquito hence needs to get blood, there are features in the blood of infected individuals that make this the preferred nutrition for the female mosquito. It has been found that the feeding time is shortened by a whole minute when mosquitoes fed on malaria infected mice, and there are theoretical bases to hold that the mechanics of blood extraction by mosquitoes would favour blood with a lower red blood corpuscle content, a feature of malaria infected blood.

Wang and Zhao hence factored the preference of mosquitoes to go for malaria infected over malaria susceptible targets into the mathematical model. The model analyses the fraction of the population that is infected, and is hence a source of pathogens, and then the susceptible fraction, which is the field for infected mosquitoes to successfully infect, the lifetime of mosquitoes, the time it takes for the parasite to get active, the breeding time of mosquitoes and the probability of mosquitoes going for infected or non-infected targets. The model then arrives at an expression that would indicate whether the infection would rise in the community or decline. We can see that with a rise in the number of infected targets, the number of mosquitoes that are capable of infecting targets would increase, but this would also limit the number of those susceptible, for new infections. There would also be the reduction of the number of all targets with time, both by natural attrition as well as a result of the disease. At what level the addition to the numbers infected would stop rising, or would start falling, or fluctuate, would depend on the preference that the mosquitoes show for infected hosts. The net result of the study was then the development of a measure, which is called the Reproduction Ratio, whose value, either less or greater than one, indicates whether the disease would die out or stabilise at a positive, periodic state.

The important things learnt from the analysis are the importance of the ambient temperature and the Extrinsic Incubation Period, the time for the parasite to mature within the mosquito. While the dependence on temperature points to another danger that would increase with global warming, the dependence on the incubation period is an invitation to scientists to develop drugs that infected persons could take and thereby affect the internal processes of mosquitoes that feed on them – a case of the human hosts becoming the vectors for administering the drug to the mosquito.

The growth of the infection is also seen to depend on the ratio of the preference of mosquitoes to bite infected persons over susceptible persons. If the medium by which this condition is communicated to mosquitoes were discovered, scientists could design ways to steer mosquitoes away from susceptible targets and hence the disease itself towards extinction.

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