A natural analytical framework for considering the effects of temperature on malaria transmission intensity is provided by deterministic models for the disease's basic reproductive number, R 0 , defined formally as the expected number of new cases arising in a naive population after one generation of the parasite from the introduction of a single infectious person [39 -41 ]. These models parameterise malaria transmission in terms of characteristics of, and interactions between, human, vector, and parasite populations [42 -46 (link)]. Those aspects of the transmission cycle affected by temperature are encapsulated in a component of R 0 known as vectorial capacity [47 (link)], V , which defines the total number of subsequent infectious bites arising from a single person-day of exposure and is classically expressed as:
where m is the number of mosquitoes per human, a is the human feeding rate, p is the daily vector survival rate, and n is the time required for sporogony, the maturation of parasites ingested by mosquitoes during human blood meals into the sporozoite life cycle stage infectious to humans. Expressing vector survival in terms of daily death rate, g where, g = -ln p, and holding constant the rate of adult mosquito recruitment, λ, relative to the human population so that, m = λ/g, vectorial capacity can be rewritten [48 (link)] as:
Temperature can influence all of the terms in this equation. Temperature affects feeding rates, a for example, via effects on vector activity and blood meal digestion [49 -51 ]. Larval ecology and, thus, adult recruitment, λ, are affected by temperatures found in aquatic habitats which play a role in modulating larval development rates and survival [33 (link),34 (link),52 (link),53 ]. Other work has demonstrated how these factors alone can impose limits on habitat suitability for particular anopheline species [53 ]. Adult mosquito recruitment is, however, also driven by a myriad of other climatic and local environmental factors, in particular those associated with the often transitory availability of aquatic oviposition sites. Here we focus on the more pronounced and directly measurable effects of temperature on vectorial capacity: the interaction between vector lifespan, determined by, g and the duration of sporogony, a. Holding a and λ constant, then, we can modify equation (2) to obtain an expression as a function of temperature, T:
Since a and λ are unknown, vectorial capacity cannot be evaluated directly, so we define instead an index of temperature suitability Z(T) that is linearly proportional to V(T) and therefore sufficient for exploring the relative, rather than absolute, effect of temperature on vectorial capacity and, thus, on R 0 . The index Z(T) can be interpreted as a relative measure of the number of infectious mosquitoes supported in an environment with temperature T, given a constant emergence rate λ. All other things being equal, an environment with, say Z(T), a value of 100 would support twice the vectorial capacity or, equivalently, require half as many vectors to support the same vectorial capacity as one with a Z(T) value of 50. Locations in which Z(T) is zero indicate that no vectors survive long enough to accumulate sufficient degree days for sporogony.
where m is the number of mosquitoes per human, a is the human feeding rate, p is the daily vector survival rate, and n is the time required for sporogony, the maturation of parasites ingested by mosquitoes during human blood meals into the sporozoite life cycle stage infectious to humans. Expressing vector survival in terms of daily death rate, g where, g = -ln p, and holding constant the rate of adult mosquito recruitment, λ, relative to the human population so that, m = λ/g, vectorial capacity can be rewritten [48 (link)] as:
Temperature can influence all of the terms in this equation. Temperature affects feeding rates, a for example, via effects on vector activity and blood meal digestion [49 -51 ]. Larval ecology and, thus, adult recruitment, λ, are affected by temperatures found in aquatic habitats which play a role in modulating larval development rates and survival [33 (link),34 (link),52 (link),53 ]. Other work has demonstrated how these factors alone can impose limits on habitat suitability for particular anopheline species [53 ]. Adult mosquito recruitment is, however, also driven by a myriad of other climatic and local environmental factors, in particular those associated with the often transitory availability of aquatic oviposition sites. Here we focus on the more pronounced and directly measurable effects of temperature on vectorial capacity: the interaction between vector lifespan, determined by, g and the duration of sporogony, a. Holding a and λ constant, then, we can modify equation (2) to obtain an expression as a function of temperature, T:
Since a and λ are unknown, vectorial capacity cannot be evaluated directly, so we define instead an index of temperature suitability Z(T) that is linearly proportional to V(T) and therefore sufficient for exploring the relative, rather than absolute, effect of temperature on vectorial capacity and, thus, on R 0 . The index Z(T) can be interpreted as a relative measure of the number of infectious mosquitoes supported in an environment with temperature T, given a constant emergence rate λ. All other things being equal, an environment with, say Z(T), a value of 100 would support twice the vectorial capacity or, equivalently, require half as many vectors to support the same vectorial capacity as one with a Z(T) value of 50. Locations in which Z(T) is zero indicate that no vectors survive long enough to accumulate sufficient degree days for sporogony.
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