A LITTLE ETYMOLOGY WHAT IS MALARIA? MALARIA LIFE CYCLE MALARIA FACTS HOW WE MODEL MALARIA IN S.I.R. MODELS
WHAT IS MALARIA? • An infective disease caused by protozoan parasites that are transmitted through the bite of an infected Anopheles mosquito; marked ...
WHAT IS MALARIA? • An infective disease caused by protozoan parasites that are transmitted through the bite of an infected Anopheles mosquito; marked by paroxysms of chills and fever
MALARIA FACTS • • • • •
A LITTLE ETYMOLOGY • The term malaria dates back to the mid 18’th century • It is credited to the Italian physician Francesco Torti • The name means “bad air” mala = bad and aria = air
MALARIA LIFE CYCLE
Causal agents are Plasmodium sp. Mosquito vectored (Anopheles sp.) 300,000 new human cases/year Kills > 700,000/yr Most victims are children
HOW WE MODEL MALARIA • Classic approach is to build S.I.R. models: – Susceptible – Infected – Recovered
IN S.I.R. MODELS • We classify individuals according to their state and then use mathematical functions to determine transition rates between states (e.g. S ➔ I )
IN S.I.R. MALARIA MODELS
MALARIA MODEL VARIABLES X Y Z b α ν β γ
• There are 5 classes, 3 for humans (S.I.R.) and for mosquitoes (S.I.)
X Y b α
CLASSIC MALARIA THEORY … dX
dt
= !"
Y X + (b + # )Y + (b + $ ) Z N
Healthy but susceptible Infected Recovered and immune Natural mortality rate Diseased mortality rate Recovery rate Biting rate Immunity loss rate N=X+Y+Z
CLASSIC MALARIA THEORY …
dX Y = ! " X + (b + # )Y + (b + $ ) Z dt N dY Y = " X ! (b + # + % )Y dt N
CLASSIC MALARIA THEORY … dX dt
= !"
Y X + (b + # )Y + (b + $ ) Z N
dY Y = " X ! (b + # + % )Y dt N dZ = %Y ! (b + $ )Z dt
CLASSIC MALARIA THEORY •…
dX Y = ! " X + (b + # )Y dt N dY Y = " X ! (b + # )Y dt N
BASIC REPRODUCTIVE RATE N !2 N R0 = b + " + b ( ) ( +" +#)
VECTORIAL CAPACITY
m! 2 " n C= # ln " Where: m = mosquito/human ratio, β = biting frequency, p = survival, n = length of cycle
VECTORIAL CAPACITY
ANOPHELES BIOLOGY
m! 2 " n C= # ln " Where: m = mosquito/human ratio, β = biting frequency, p = survival, n = length of cycle
PREDIURESIS
MOSQUITO NUTRITIONAL ECOLOGY • What mosquitoes eat and why
SOME “FACTS” • Mosquitoes feed on sugar to maintain somatic (body) function • Mosquitoes feed on blood for gametic (reproduction) function • Sugar feeding trades off with blood feeding • Sugar feeding impacts survivorship and blood feeding
WHAT ABOUT SUGAR? • The conclusion: • Plant feeding is rare and trivial for An. gambiae (and other mosquitoes closely associated with humans) BUT • There are lots of reasons to believe otherwise
AND!!! • Nearly every mosquito lab that I know of provides sugar to adult mosquitoes. WHY?
WHAT ABOUT SUGAR? • The word on the street: – An. gambiae can allocate energy from human blood to soma – Nectar feeding is rarely observed – Fructose-positive samples are not common (e.g. 20% Beier 1996)
WHAT ABOUT SUGAR? • BUT: • Without knowing sugar digestion rates, frequency of fructose positivity is meaningless • Behaviors that are not frequently expressed are not necessarily trivial • Feeding on humans is dangerous
VECTORIAL CAPACITY
m! 2 " n C= # ln " Where: m = mosquito/human ratio, β = biting frequency, p = survival, n = length of cycle
ENERGY PROFILES IN NATURE
LIFE IS TOUGH
Reserves
• Energy is in short supply for Anopheles.
TWO MORE FACTS • Under nutrient stress, female mosquitoes reallocate resources away from survival and towards reproduction • Nutrition state can affect the impact of Plasmodium on female survival
CONTROLLED EXPERIMENT • Give female mosquitoes choice of blood host and nectar host odors
THE SMOKING GUNS • • • •
Observations Crop collections Digestion rates Frequency estimates
A CLEAR PREFERENCE
CLASSIC ASSUMPTION
AN OBSERVATION • Everybody is plastic
• Mosquito behavior is hardwired and invariant • Recall, we assumed that beta was a constant but if sugar alters beta then it isn’t
VARIABILITY IN NATURE • …
HOW TO EXPLOIT ENERGY VARIABILITY IN NATURE • Employ bednets in the context of mosquito energy budget constraints….
A MINI VILLAGE • …
TESTING THE THEORY • •Our …. mini domicile
HOW TO EXPLOIT ENERGY VARIABILITY IN NATURE • Employ bednets in the context of mosquito energy budget constraints