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 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 FACTS • Causal agents are Plasmodium sp. • Mosquito vectored (Anopheles sp.) • 300,000 new human cases/year • Kills > 700,000/yr • Most victims are children MALARIA LIFE CYCLE 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 )
Transcript
WHAT IS MALARIA?
• An infective disease caused by protozoanparasites that are transmitted through thebite of an infected Anopheles mosquito;marked by paroxysms of chills and fever
A LITTLE ETYMOLOGY
• The term malaria dates back to the mid18’th century
• It is credited to the Italian physicianFrancesco Torti
• The name means “bad air” -mala = bad and aria = air
MALARIA FACTS
• Causal agents are Plasmodium sp.• Mosquito vectored (Anopheles sp.)• 300,000 new human cases/year• Kills > 700,000/yr• Most victims are children
MALARIA LIFE CYCLE
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 totheir state and then use mathematicalfunctions to determine transition ratesbetween states (e.g. S ➔ I )
IN S.I.R. MALARIA MODELS
• There are 5 classes, 3 for humans(S.I.R.) and for mosquitoes (S.I.)
MALARIA MODEL VARIABLES
X X Healthy but susceptibleY Y InfectedZ Recovered and immuneb b Natural mortality rateα α Diseased mortality rateν Recovery rateβ Biting rateγ Immunity loss rate N = X + Y + Z
CLASSIC MALARIATHEORY
… dXdt
= !"YNX + b + #( )Y + b + $( )Z
CLASSIC MALARIATHEORY
… dXdt
= !"YNX + b + #( )Y + b + $( )Z
dYdt
= "YNX ! b + # + %( )Y
CLASSIC MALARIATHEORY
… dXdt
= !"YNX + b + #( )Y + b + $( )Z
dYdt
= "YNX ! b + # + %( )Y
dZdt
= %Y ! b + $( )Z
CLASSIC MALARIATHEORY
• …dXdt
= !"YNX + b + #( )Y
dYdt
= "YNX ! b + #( )Y
BASIC REPRODUCTIVE RATE
R0 =! 2NN
b + "( )+ b + " + #( )
VECTORIAL CAPACITY
Where: m = mosquito/human ratio, β = bitingfrequency, p = survival, n = length of cycle
C =m! 2"n
# ln "
VECTORIAL CAPACITY
Where: m = mosquito/human ratio, β = bitingfrequency, p = survival, n = length of cycle
C =m! 2"n
# ln "
ANOPHELES BIOLOGY
PREDIURESIS MOSQUITO NUTRITIONALECOLOGY
• What mosquitoes eat and why
SOME “FACTS”
• Mosquitoes feed on sugar to maintainsomatic (body) function
• Mosquitoes feed on blood for gametic(reproduction) function
