Foreword
Contributors
I Background
1
The Study of Malaria Control
1.1
The Prevention of Malaria
1.2
The Quantitative Approach
1.3
Larval Source Management
1.4
Malaria Population Dynamics
1.5
Measuring Transmission
1.6
The Study of Epidemics
1.7
Mathematical Epidemiology
1.8
Approaching Complexity
1.9
Historical Notes
1.9.1
The Light Microscope
1.9.2
Mathematical Epidemiology Before Ross
2
Basic Malaria Models
2.1
Ross’s Quantiative Logic
2.2
Deterministic, Discrete-Time
2.2.1
Model
2.2.2
Solutions
2.2.3
Analysis
2.3
Computation
2.3.1
Functions
2.3.2
Verification
2.4
Events and Counting
2.4.1
On not not getting infected
2.4.2
ross_dts_2
2.5
Stochastic, Discrete Time
2.6
Deterministic, Continuous Time
2.6.1
ross_xde
2.6.2
Rates
vs.
Proportions
2.6.3
Solutions
2.6.4
Computation & Visualization
2.6.5
Steady States
2.6.6
Verification
2.6.7
Thresholds
2.7
Stochastic, Continuous Time
2.8
Mathematical Species
2.8.1
Deterministic Models
2.8.2
Stochastic Models
2.9
Notes
3
The Ross-Macdonald Model
3.1
Infection
3.2
Mosquito Bionomics
3.3
Equations
3.4
Solutions
3.5
The Basic Reproductive Number
3.6
Sensitivity to Parameters
3.7
Vectorial Capacity
3.8
Classifying Transmission
3.9
History
3.9.1
Lotka
3.9.2
Macdonald and Medical Entomology
3.9.3
\(R_0\)
in the GMEP
4
Malaria Metrics
4.1
Malaria Epidemiology
4.1.1
Infection Prevalence
4.1.2
Infection Incidence
4.1.3
Drug Taking
4.1.4
Disease
4.1.5
Serology
4.2
Mosquito Ecology
4.2.1
Entomological Inoculation Rates
4.2.2
Bionomics
4.3
Transmission
4.3.1
Infectiousness
4.3.2
Vectorial Capacity
4.3.3
Transmission Efficiency
4.4
Surveillance
4.5
Notes
5
Models and Data
5.1
Observational Processes
5.2
Skill Sets
5.3
Simulation Studies
5.4
State Space Modeling
5.5
Parameter Estimation
5.6
Malaria Intelligence
5.7
Model Calibration
6
Research and Policy
6.1
Temporal Epochs
6.2
Information and Decisions
6.3
Inference
6.4
Imputation
II The Toolbox
7
Malaria Models for Policy
7.1
Human Malaria Infection and Immunity
7.2
Human Demography
7.3
The Burden of Malaria
7.4
Mosquito Ecology and Behavior
7.5
Blood Feeding and Transmission
7.6
Theory for Vector Control
7.7
Spatial Dynamics and Connectivity
7.8
Parasite Diversity
7.9
Evolution of Drug Resistance
7.10
Evolution of Insecticide Resistance
8
Heterogeneous Transmission
8.1
Heterogeneous Biting
8.2
Blood Feeding
8.2.1
Mosquito Searching
8.2.2
Risky Human Behaviors
8.3
Environmental Heterogeneity
9
Human Aging & Demography
9.1
Cohort Dynamics
9.2
Gallerkin
10
Adult Mosquito Dynamics
10.1
Emergence
10.1.1
Variables
10.1.2
Blood Fed Mosquitoes
10.1.3
Infected Mosquitoes
10.1.4
Infectious Mosquitoes
10.1.5
Infected Humans
10.1.6
…as a System
10.1.7
Solutions
10.1.8
Initial Values
10.1.9
Parameter Values
10.1.10
Solving
10.1.11
Visualizing
10.2
Steady States
10.2.1
Mosquito Density
10.2.2
EIR
10.2.3
Vectorial Capacity
10.2.4
Malaria Prevalence & Thresholds
10.2.5
Checking our Work
10.3
Stable Orbits
10.3.1
Thresholds
10.3.2
Orbits
10.3.3
Average Dynamics
11
Mosquito Ecology
11.1
Egg Laying
III Malaria Modeling
12
Model Building
12.1
Compartment Models
12.2
Primary Model Development
12.3
Implementation and Verification
12.3.1
Solving
12.3.2
Mathematical Analysis
12.3.3
Simulation
12.4
What is a Model?
12.5
Accuracy & Validation
12.5.1
Validation Points
12.6
The Measure of a Model
12.6.1
Limitations
12.6.2
Parsimony
12.7
Secondary Model Development
12.8
Conclusions
13
Uncertainty
13.1
What we Don’t Know about Malaria
13.2
What we Don’t Know about Malaria
14
Realism
14.1
Malaria Epidemiology
14.2
Transmission
14.3
Mosquito Ecology
14.3.1
Resource Availability
14.3.2
Egg Laying
14.3.3
Regulation
14.3.4
Exogenous Forcing
14.4
Heterogeneity & Stratification
14.4.1
Strata in the Ross model
14.4.2
Frailties
14.4.3
Age
14.5
Spatial Dynamics
14.5.1
Human Migration, Mobility & Travel
14.5.2
Mosquito Search & Dispersal
14.5.3
The Mixing Matrix
14.5.4
Pathogen Dispersal by Humans
14.5.5
Pathogen Dispersal by Mosquitoes
14.6
Exogenous Forcing
14.6.1
Weather
14.6.2
Habitat Dynamics
14.6.3
The EIP
14.6.4
Seasonality
14.7
Integrated Vector Control
14.8
Integrated Malaria Control
14.9
Context
15
Modularity and Software
15.1
Model Building
15.2
Modular Computation
15.2.1
exDE
15.3
Notes
15.3.1
Why use densities?
IV Malaria Epidemiology
16
Malaria Epidemiology
16.1
Life Stages
16.2
Overview
16.3
Infection
16.3.1
Duration
16.3.2
Detection
16.3.3
Superinfection
16.4
Disease & Immunity
16.5
Gametocytes and Infectiousness
16.6
Treatment and Chemoprotection
16.6.1
The Time Course of an Infection
16.6.2
Intrahost Models
16.6.3
Synthesis
17
Stage-Structured Infection
17.1
Stages of Infection
17.2
Controlled Infections
17.2.1
Malariotherapy
17.2.2
CHMI
17.3
A Simple Infection
17.3.1
Time Course
17.3.2
Duration
17.4
Superinfection
17.5
Process
vs.
Observation
17.5.1
Detection
18
Superinfection
18.1
Queuing Models
18.2
Macdonald’s Superinfection Model
19
Stage-Structured Malaria Infections
19.1
Stages of Infection
19.2
Controlled Infections
19.2.1
Malariotherapy
19.2.2
CHMI
19.3
A Simple Infection
19.3.1
Time Course
19.3.2
Duration
19.4
Superinfection
19.5
Process
vs.
Observation
19.5.1
Detection
20
Stage-Structured Immunity
20.1
The Garki Model
20.2
Stage-Structured Immunity
20.3
Strain Specific Immunity
20.4
Memory Tracking
20.5
Age
vs.
Prevalence
21
Age-Structured Infection Models
22
Treatment and Chemoprotection
22.1
Curing Infections
22.2
Chemoprotection
22.3
Adherance
22.4
Treatment Rates
23
Queuing Models
24
Hybrid Models
25
Fever and Severe Disease
25.1
Fever
25.2
Anemia
25.3
Severe Disease
26
Gametocytes and Infectiousness
26.1
Gametocytemia
26.2
Anti-Gametocyte Immunity
27
Within Host
28
Models and Malaria Epidemiology
28.1
V Mosquito Ecology
29
Mosquitoes
29.1
Aquatic Dynamics
29.1.1
Equations
29.1.2
Solutions
29.1.3
Regulation
29.2
Understanding Mosquito Dynamics
30
Behavioral State Models
31
Regulation of Mosquito Populations
32
Mosquito Dispersal
33
Mosquito Age
34
Multi-Species Models
34.1
Vector Competence
35
Aquatic Ecology
36
Mosquito Larval Stages
37
Resource-Based Competition
38
Habitat Dynamics
39
Temporal Dynamics
39.1
Exogenous Forcing
39.2
Mosquito Survival through the EIP
40
Measuring Mosquitoes
VI Transmission
41
Blood Feeding and Transmission
41.0.1
Search and Risk
41.0.2
Search Weights and Availability
41.0.3
Functional Response
41.0.4
Environmental Heterogeneity
41.1
Host Availability
41.2
Blood Feeding Rates
41.3
The Human Fraction
41.4
The Mixing Matrix,
\(\beta\)
42
Human Mobility
42.1
Modalities
42.2
Time at Risk
42.3
Travel
42.4
Migration
43
Spatial Dynamics
44
Spatial Heterogeneity
44.1
Overview
44.1.1
Age
44.1.2
Location
44.1.3
House Type
44.1.4
Activities
44.2
Frailty
44.3
Environmental Heterogeneity
45
Stratification
45.1
Stratifying Human Populations
45.2
Spatial Units
VII Malaria Control
46
Malaria Control
46.1
Health Systems
46.2
Vector Control
47
Insecticide-Treated Bednets
48
Indoor Residual Spraying
49
Larval Source Management
50
Attractive Toxic Sugar Baits
51
Integrated Vector Control
VIII Health Systems
52
Cohort Dynamics
52.1
Boxcar Models
52.2
Delay
53
Human Demography
53.1
Migration
54
Human Travel and Malaria Importation
55
Stratification
56
Pharmaceutical Interventions
56.1
SMC
56.2
MDA
56.3
Drugs
56.4
Vaccines
IX Analytics
57
Malaria Analytics
57.1
The Burden of Malaria
57.2
A Theory of Control
57.3
Generic
vs.
Specific Advice
57.4
Imputation
57.5
Robust Analytics
58
Measuring Malaria for Control
58.1
Realistic Bounds
58.2
The Local Fraction
58.2.1
Travel
58.2.2
Mobility
58.3
Drug Taking
58.4
Seasonality
58.5
Frailty
58.6
Environmental Heterogeneity
58.7
Pf
EIR
vs.
Pf
PR in Data
58.8
Pf
EIR
vs.
Pf
FoI in Data
58.9
Synthesis
59
Discrete Time
60
Spatial Concepts and Connectivity
61
Mosquito Microecology
62
Microsimulation
63
Spatial Control
64
Model Libraries
65
Base Models
66
Built-in Analytics
67
Stochasticity
68
A Glossary
X Supplements
69
References
Applied Malaria Dynamics
14.9
Context