simulation model for spread of dengue infection in the

THE Countryside Development RESEARCH JOURNAL

An official peer-reviewed journal published by SAMAR STATE UNIVERSITY 171

Abstract

I. INTRODUCTION

Simulation Model for Spread ofDengue Infection in the Countryside

Elmer A. IreneCollege of Education, Samar State University, Catbalogan City

[email protected]

This paper attempts to develop a simulation model that would predict the spread of infection of dengue cases in the countryside specifically in Samar, Philippines based on the given number of assumptions and random data. The study used an experimental design using simulation modeling. Assumptions were formulated to measure different variables. Findings revealed that transmission of dengue from one victim to other people proliferates when the probability of exposure to dengue is high and if there is minimal intervention program for the spread of dengue cases.

Keywords: simulation model, mosquito, dengue, transmission model

There are factors that contribute to the spread of dengue infections in most of the tropical regions. These are biological and environmental factors which contribute to high levels of biodiversity in hosts, vectors, and pathogens, and social factors that reduce efforts to control diseases (Sattenspiel, 2000). The incident is more pronounced in a community with poor and lacking health and sanitation (Resurgence, 2008; Guzman, 2004; Esteva & Vargas, 1999)in which it affected many coming from poor countries (Guha-Sapir & Schimmer 2005 ).More often than not, people rather than vectors are primarily responsible for the dissemination of the disease (Harrington, 2005; Sattenspiel, 2000).

Chikungunya and Dengue fever are viral diseases transmitted to humans by the bite of infected Aedes Aegypti (the yellow fever mosquito) and Aedesalbopictus (the Asian tiger mosquito). The incubation period can be 2-12 days but is usually 3-7 days. They proliferate further because of occurrences of “silent” infections or

infections without illness which make it more likely to spread more infection (Halstead, 2008; Méndez, et.al., 2006; Wilson,1995).It implies that the victim is not aware that he is already a carrier of the virus, thus, he does not take precautionary measure not to be bitten by a mosquito. Unfortunately, in the rural communities, there is still a good number of people who do not know about the mode of infection of dengue and even if the victim is aware. However, there is no correlation between his knowledge and his preventive practices (Yboa & Labrague, 2013; Hairi, et.al., 2003).

The spread of infection is caused by the bite of an infected mosquito. Mosquitoes become infected when they feed on a person infected with a virus. Infected mosquitoes can then spread the virus to other humans when they bite (http://www.who.int/denguecontrol/faq/en/index5.html). Symptoms of infection are characterized by a sudden onset of high fever, severe headache, backache, intense pain in joints and muscles, retro-orbital

An official peer-reviewed journal published by SAMAR STATE UNIVERSITY172

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pain, nausea and vomiting. A generalized erythematous rash that usually begin 4-7 days after the mosquito bite and typically last 3-10 days are observed. However, infection with a dengue virus serotype can also produce a more complex and severe form of clinical manifestations like hemorrhage and shock.

In the Philippines, despite the extensive campaign of the government against dengue and chikungunya, there are evidences of increasing rates of dengue morbidity in the recent year (Yboa&Labrague,2013). The problem is compounded with less access to information in rural areas and where unsanitary practices and dirty surroundings add to the proliferation of the disease. Just recently an outbreak of dengue fever and chikungunya was observed in Samar, Philippines. In a public health facility where said victims are admitted and given treatment, rooms are filled with patients that some of them are already occupying the lobby just to get treated. In a three-month period, there

were 86, 23 and 36 cases, in June, July and August respectively recorded cases of dengue and chikungunya in Samar provincial hospital in Catbalogan City, capital of Western Samar.

Hence, recent outbreaks of dengue in the rural communities necessitated development of this study. The knowledge that could be gained in this investigation would guide public administrators to plan, design and initiate initiatives, programs, and policies relative to dengue and chikungunya prevention. The purpose of this simulation model is to determine the spread of infection of dengue carrying mosquitoes.

A. Conceptual Framework

The study is based on the dengue transmission model and network theory as shown in Figure 1. Mosquito to human transmission is patterned from the model of Focks, et.al. (1995). Where each infected mosquito has a probability to bite different people, and the product of

Figure 1. Network scheme of dengue transmission



infected mosquitoes is multiplied by the number of people bitten which will result to new cases of dengue infection. These new cases will continue the cycle.

II. METHODOLOGY

The study made use of an experimental design using simulation modeling. The experimental criterion measure is the number of new cases (NC) emerged from the initial number of infected mosquitoes. The simulated experimental model is Xi, the dengue transmission without intervention Y1 and with intervention Y2. The emerged new cases will be the base number for the next cycle of transmission.

NC = U x PB

The factors that determine the number of new cases are the probability of being bitten, U (where it is assigned with random numbers 0 and 1) and number of people bitten by infected mosquito,PB (where PB = random numbers 0, 1, 2 and 3).

In Y1, the probability of being bitten U1 is at 60%. And the probability of PB is given at 25% equal distribution while, in Y2, the exposure probability of U1 decreases at 10% interval every month. The simulation covers a one-year period.Six runs of Simulations were conducted, and the new cases per month are the average tally of results per month.

The simulation model is based on the following assumptions:

1) Life cycle of a mosquito: 14 days in all months thus there will be two breeds of mosquitoes in a month.

2) Mode of transmission: Network and

Fock’s model of mosquito to human transmission.

3) A person has a 50/50 probability of being bitten by a mosquito in which

exposure probability is high when there was no intervention and less exposure probability, if otherwise.

4) Once bitten by mosquito, the person gets infected with the virus.

5) One mosquito may bite in his lifespan 0,1, 2 or 3 different people.

6) Exposure Probability is 60% in the rural area due to inaccessibility of information in dengue prevention or due to minimal intervention program.

III. RESULTS AND DISCUSSION

Table 1 shows the first simulation run for n=15 persons infected with dengue virus. As seen in the table, out of fifteen infected cases of dengue, only 12 emerged as new cases after a month. It was hypothesized initially that the result is higher because of the networking scheme and due to

Table 1.First simulation run for Dengue Infected cases

in one month

Legend: U - If bitten – 1, @ 60% exposure If not bitten – 0 PB - People Bitten (0,1,2,3) NC - New Cases

Infected U PB NC

1 1 1 12 1 1 13 1 0 04 0 1 05 1 1 16 0 1 07 1 2 28 1 2 29 0 3 0

10 1 3 311 1 1 112 1 0 013 0 1 014 1 1 115 0 2 0

Total New Cases 12


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the multiplicity of factors. However, one limitation of this simulation is it focuses only on one mosquito that would bite one person. If we would assume that the number of new cases may occur twice or thrice the number due to multitude of mosquitoes around, then it would be probably higher. Moreover, one mosquito may not bite victim number 4. But that same mosquito can get a chance to bite him in the next day or other days in a month, assuming that it has 5 to ten days mature lifespan. Thus, the result may be

Figure 2: Random Distribution of N persons bitten by a dengue carrying mosquito

higher.

As shown on figure 2, majority of infected persons were not bitten by a dengue carrying mosquito while only one mosquito had bitten three persons in its lifetime.

The average new case of dengue in a month is determined from the six simulation runs of the same number of samples. The exposure probability, U, is held at constant value of 60% every month considering that there was no intervention conducted. Random numbers were obtained through the random distribution assigned by the computer software.

As can be gleaned from the data shown on table 2, there was no single month that the average number of cases is greater than 15, the initial number. But looking at simulation run number 3, all the new cases are above 15. Also, there were months that cases of infection are high, and there were months where it was few.

Revealed in Table 3 that out of 15 infected cases of dengue, only three cases remained after five months. It can be attributed to the intervention efforts

Table 2.Simulation runs in a one-year period (Without Intervention, Y1)

MonthsSimulation Runs

Average1 2 3 4 5 6

1 15 15 15 15 15 15 152 12 4 21 15 12 8 123 8 3 24 12 15 4 114 14 2 16 7 11 6 95 15 0 16 4 14 1 86 14 0 24 6 18 0 107 15 0 30 7 13 0 118 11 0 29 10 11 0 109 10 0 26 10 2 0 8

10 8 0 31 10 1 0 811 7 0 15 3 2 0 512 7 0 15 1 1 0 4



Table 3. Simulation runs in a one-year period (Without Intervention, Y1)

Months EPRun

Average1 2 3 4 5 6

1 0.6 15 15 15 15 15 15 152 0.5 21 17 13 13 10 13 153 0.4 16 12 13 10 14 9 124 0.3 11 11 7 7 5 0 75 0.2 6 11 8 12 1 0 66 0.1 5 3 0 8 0 0 37 0.1 2 3 0 0 0 0 18 0.1 0 0 0 0 0 0 09 0.1 0 0 0 0 0 0 0

10 0.1 0 0 0 0 0 0 011 0.1 0 0 0 0 0 0 012 0.1 0 0 0 0 0 0 0

conducted to prevent new occurrences of dengue infections that resulted to less exposure or a chance to be bitten by a dengue-carrying mosquito. It can also be extrapolated from the table that if intervention programs are sustained, there will be a positive control of this disease.

IV. CONCLUSIONS AND RECOMMENDATIONS

The simulation looked into how the network theory and dengue transmission model can be portrayed through random numbers governing the given assumptions. It is seen that the trend of data of the number of new cases is declining with the model with intervention program having steeper decline, which is a positive indication. However, the simulation is limited in terms of the number of mosquitoes considered in the study and the exact number of infected persons. The result may vary if a greater number of mosquitoes are considered but for simplicity and traceability of simulation, only the above assumptions are considered in the model. Considering the significance of the result, it contributes

to mathematical modeling of the dengue transmission. In which it can provide insights and regulation when devising operational program for a complicated and nonlinear system (Massad, 2008; Focks, et.al., 2005; Newton, 1992).

In dengue transmission, it is confirmed that the lesser the exposure probability to get bitten by a mosquito, the lesser the chance to spread the infection. Hence, it is strongly recommended to maintain the intervention programs to prevent occurrences of new cases such as to get rid of the breeding sites so that mosquitoes do not have a chance to breed. A person with chikungunya or dengue fever should strive not to be exposed to mosquito bites to avoid further spreading the infection. The person should stay indoors and must be protected from mosquito bites such as wearing long-sleeves and use of repellent on exposed skin.

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simulation model for spread of dengue infection in the

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