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Epidemic Enhancement Nature of Chikungunya Fever

Authors:

K Moheeput

SK Ramchurn

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Chikungunya Fever

Chikungunya fever is a vector borne disease caused mainly by the aedes aegypti mosquito.

Although aedes aegypti is usually considered to be the primary mosquito vector for Chikungunya virus, aeded albopictus has been the incriminated vector during the 2005-2006 epidemics in Reunion Island and Mauritius.

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The dynamics of the 2006 outbreak of Chikungunya fever in Mauritius with different level of acquired immunity was widely studied by Ramchurn et al.

In their study they showed that herd immunity threshold would have been reached in a population size of 3000 inhabitants if about 60 % of the population had been affected.

Studying the 2006 Chikungunya Fever Outbreak in Mauritius

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Epidemic Enhancement

In 2006, Savill et al studied the dynamics of the spread of H5N1 avian influenza into a vaccinated poultry population using a detailed stochastic model.

They found that the vaccinated poultry population could promote undetected pathogen persistence, facilitating “silent” spread to neighboring farms.

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Epidemic Enhancement (cont)

Pulliam et al carried out a study in 2007 and they showed that some diseases have a long epidemic duration when they are introduced in a population with a certain level of acquired immunity.

They called this phenomenon of long epidemic duration as “epidemic enhancement”.

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Investigating the possibility of Epidemic Enhancement nature of Chikungunya Fever

Aim of study

7Schematic diagram of the SEIR compartmental human mosquito interaction model

SEIR Model

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Exposed Host

Infected Host Recovered HostSusceptible Host

Susceptible VectorInfected Mosquito

Exposed Mosquito

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Symbols and Parameter value

Parameter Symbol Value

Life span of human 25000 days ( 70 Years)

Life span of vector (mosquito) 30 days

Product of vector biting rate and the probability of transmission of virus from vector to human

Latent period for human 2.5 days

Latent period for vector 4 days

Human infection period 3 days

Ratio of female mosquito to human 3

hm/1

vm/1

hvC

hvvh CC

hK/1

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Forecasted evolution of Chikungunya fever outbreak in a locality with a population density of 10000 per sq. km with initially 3 infected humans and 80 % of the human population in recovered state.

0 50 100 150 200 250 300 350 4000

10

20

30

40

50

60

70

80

90

Time (in days)

0 10 20 30 400

2

4

6

8

10 number of infected mosquito

number of infected human

number of infected human

It was found that the number of infected human increases very slowly, making the epidemic almost undetectable and also longer in duration.However, there is one feature shown in this graph which is biologically implausible: from time t=5 to t=40 the number of infected (and infectious) human was less than 1 but still the number of infected mosquito continues to increase.

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Computed evolution of Chikungunya fever outbreak in a locality with a population density of 10000 per sq. km with initially 1 infected human

0 1000 2000 3000 4000 5000 60000

1000

2000

3000

4000

5000

6000

7000

time (in days)

0 100 200 3000

2000

4000

6000

5300 5400 5500 56000

100

200

300

400

2900 2920 2940

-1

-0.5

0

0.5

1

x 10-6

infected human

infected mosquito

A B C

Graph A shows the number of infected human and mosquito during the epidemic explosion, graph B shows that the number of infected human and mosquito are less than 1 but never constantly zero after the epidemic explosion, while in graph C we show the second epidemic outbreak after the human susceptible population has been replenished. This is because individuals are treated as being continuous in this model.

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Implementing of the Stochastic SEIR Model

Solution to the problem is to treat human and mosquito as discrete quantity.

The stochastic model is set up using the idea put forward by Gillespie in 1977 when he developed the stochastic simulation algorithm to study the time evolution of a spatial homogeneous system of couple chemical reactions.

To apply the Gillespie stochastic simulation algorithm to the SEIR model, we have to write the propensity function for each reaction equation governing the epidemiological and the time step for the successive reaction.

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Reaction Equation and Propensity Function

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Reaction Equations Propensity Functions

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Forecasted evolution of Chikungunya fever outbreak in a locality with a population density of 10000 per sq. km with initially 3 infected humans and 80 % of the human population in recovered state.

0 50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

Time( in days)

0 10 20 30 400

1

2

3

4

5

6

7

8

9

10number of infected human

number of infeceted mosquitonumber of infected human

The subgraph shows the variation of the number of infected mosquito and human for the first 45 days. A fluctuation in the number of both populations in the infected state is observed. With the number of human and mosquito being discrete, this situation is biologically plausible.

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Computed evolution of Chikungunya fever outbreak in a locality with a population density of 10000 per sq. km when 1 infected human is introduced in a naïve population

0 500 1000 1500 2000 2500 30000

100

200

300

400

500

600

700

800

900

1000

Time (in days)

0 500 1000 1500 20000

5000

10000

2400 2600 2800

-5

0

5

x 10-8

0 100 200 3000

2000

4000

6000

susceptible human

infected human

infected mosquito

A

B C

It is observed that the Chikungunya virus spreads rapidly in the susceptible populations driving itself to extinction by invading the system and depleting the human susceptible pool, thus preventing the virus from future outbreak.

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From the graph of the previous slide we see that with time humans in the recovered state and mosquitoes in the infected state die and are replaced by new born in their respective population, thus the susceptible state of both population are replenished, but still there is no secondary outbreak.

We observed that when introduced in a partially immune population the Chikungunya fever virus produces a quite small epidemic outbreak with a less dramatic depletion in the human susceptible population, which allow the virus to persist in the population thus extending the duration of the epidemic.

This observation shows the “epidemic enhancement” characteristic of the Chikungunya fever virus.

Observation

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0.5 0.55 0.6 0.65 0.7 0.75 0.80

200

400

600

800

1000

1200

1400

1600

1800

2000

Proportion of human population immune when 3 infective humans enter the population

Avera

ge n

um

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of

infe

cte

d p

eople

by t

he e

nd o

f 100 d

ays

Stochastic SEIR model

Deterministic SEIR model

Comparing Stochastic and Deterministic models Result

The average number of infected human by the end of 100 days is computed for different proportion of the human population immune when 3 infective humans are introduced in a locality of 10000 inhabitants per sq. km. For the stochastic model the simulation was run 20 times for each level of initial population immunity and the average was then computed.

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The result shown in the previous slide indicates that an increase in the proportion of the human population with acquired immunity decreases the number of infected human by the end of 100 days, thus facilitating the “silent’ spread” of the disease.

The presence of immune individuals indeed results in a lower force of infection upon re-introduction of infected human with Chikungunya virus. The epidemic enhancement nature of Chikungunya fever virus may have important implication for Mauritius. Some districts and coastal areas like Triolet, Riviere du Rempart, Pamplemousse and Roches Noires were the most affected regions during the severe Chikungunya fever outbreak during the months of January to April 2006. Most of these regions now contain human population with quite a high proportion of inhabitant with acquired immunity.

Discussion

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If one or few humans infected with Chikungunya virus enter these regions, the virus persistence within these isolated populations will increase the time span over which movement of individuals may spread the disease to new areas and may also decrease the probability that the infection will be detected.

Thus, regions which are known to have been infected with Chikungunya virus must be considered to pose substantial risk despite the fact that they are currently free from infection.

Discussion (cont)

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•WHO Epidemic and Pandemic Alert and Response (EPR). Chikungunya in La

Réunion (France), Mayotte, Maurice, Seychelles and India.

•Available online at: http://www.who.int/csr/don/2006_03_17/en, accessed on 30

May 2007

•Chretien J-P, Anyambe A, Bdno SA, Breiman RF, Sang R et al. Drought-

associated Chikungunya emergence along coastal East Africa. AM J Trop Med Hyg

2007;76:405-7

•Chateau T. Chikungunya: Plan d’action pour l’hiver. L’Express Vendredi 5 Mai

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•Boëlle P-Y, Thomas G, Vergu E, Renault P, Valleroni A-J and Flahault A.

Investigating transmission in a two-wave epidemic of Chikungunya fever, Réunion

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•Ramchurn S-K, Goorah SSD, Mungla D, Ramsurrun B, Pydiah V and Summun A.

2006. A study of the 2006 epidemic outbreak in Mauritius.

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