Reproductive Model 08 June v3

A weather-based mathematical and simulation model for Aedes Aegypti reproductive life cycle

Mohammad Amin Khana,b*, Muhammad Asif Alia,b, Shahid Latifa,b, Muhammad Naeem Ayyaza,b

aDepartment of Electrical Engineering, University of Engineering and Technology, Lahore, Punjab.bCentre for System Simulation and Visual Analytics Research (C-SVAR), KICS, UET, Lahore, Punjab.

*Corresponding author: [email protected]

Abstract—After the dengue outbreak of 2011, the Punjab government in Pakistan took initiatives for dengue prevention and control in 2012, leading to a substantial decrease in the number of dengue cases in 2012. However, in 2013 a rising trend of dengue patients was again observed. The cause for this increase has been the uncontrolled dengue mosquito population that thrives in tropical and subtropical regions with a humid environment. To understand in particular the population dynamics of Aedes Aegypti, we have devised a mathematical model that illustrates dengue reproductive life cycle through the seasonal variation in weather conditions, i.e. temperature and rainfall. This model is formulated using ordinary differential equations based on the concept of compartmental modelling. Proposed model is implemented as software simulation, using system dynamics approach to obtain a diurnal population trend of egg, larva, pupa, and adult on the basis of change in weather conditions, for the Lahore city in Punjab province. Through our simulation results, we observe a peak reproduction time during monsoon season, i.e. from July to September, which is validated via actual patients’ trend from August to mid-September. The model provides optimal time to depict the emergence of Aedes mosquitos’ w.r.t the changing weather conditions. It will help the government authorities in narrowing down the time for planning dengue prevention and control measures––thus subduing the dengue threats in future. It is hoped that this research will have a great impact in controlling and eliminating dengue outbreaks in Pakistan.

Key Words: Aedes aegypti, system dynamics, mathematical model, simulation, compartmental modelling

I. INTRODUCTION

Dengue Fever (DF) is a mosquito-borne viral disease prevailing in tropical and sub-tropical regions across the globe, with al -most 390 million cases each year [1]. DF is mainly caused by a small single-stranded RNA (Ribonucleic acid) virus―belonging to genus Flavivirus, transmitted through the bite of infected female mosquitos: aedes albopictus and aedes aegypti––the latter known to be the primary carrier of dengue virus [2]. In Pakistan, the occurrence of dengue fever has been reported on numerous occasions since 1994, causing major outbreaks in recent decades. Major geographical regions of Pakistan burdened with dengue epidemic include the Khyber Pakhtun Khwa (KPK) province with 3,500 cases in 2003, Sindh and Punjab provinces with 5,400 cases in 2006, and Punjab province with 5,000 cases in 2010 and over 20,000 in 2011 [3]. However, owing to disease control activities the number of dengue cases decreased substantially in 2012 [4], however a rising trend of the patients was again ob-served in the subsequent years.

In order to prevent or control future outbreaks in the region, it is important to study and understand the phenomenon respons -ible for dengue outbreaks––which in this case is the uncontrolled reproduction of Aedes mosquitos. There is a need to under-stand the dynamics of ae. Aegypti life cycle and devise an appropriate model describing its comprehensive reproductive beha-vior.

Analysis of the bionomics of aedes aegypti has been undergoing since the 20th century [5]. In 1960, S. R. Christophers ob-served in detail the effect of variation in temperature and rainfall on development and survival rates of yellow fever mosquito (ae. Aegypti) in laboratory experiments [5]. Later on in 1990, Rueda et al. [6] derived parameters from simplified Sharpe & De-Michele enzyme kinetic model [7] to determine the development rates of larva and pupa of Culex Quinquefasciatus and Ae. Ae-gypti [7]. These studies have been used to develop statistical, mathematical, and simulation models to understand the relation -ship between ae. Aegypti life cycle, its virus transmission behavior, and spatial distribution [8, 9, 10, 11].

Focks et al. developed a simulation model, named Container-Inhabiting Mosquito Simulation Model (CIMSiM) that determ-ine the reproductive behavior of ae. Aegypti based on the influence of weather conditions [12, 13]. Their model can spatially distribute natural or manmade mosquito breeding sites, which make it highly dependent on manual vector surveillance to ac -quire model parameter concerned with ae. Aegypti bionomics. M. J. Hopp and J. A. Foley presented a modified version of CIM-SiM illustrating a global-scale relationship between weather parameters and ae. Aegypti [14]. They have defined the daily mor-tality rates of aedes mosquito to be independent of temperature variation i.e. in the range of 10°C to 38°C for larva and pupa population, while 5°C to 40°C for adult mosquitoes. Otero et al. developed a stochastic model that describes the population dy-namics of ae. Aegypti during endemic situations [15, 16]. They have neglected the impact of rainfall on aedes mosquito popula-tion, because for their specific region rainfall occurs throughout the year. Due to this fact, water is available at all times and therefore, is not a dominant parameter responsible for variation in mosquito reproduction. Moreover, they have calculated the daily mean temperature based on a deterministic equation derived using historical records. This results in annually recurring patterns of temperature that leads to cyclic reproduction of aedes mosquitoes for each year. In the recent past, Morin et al. de-veloped a mosquito reproductive simulation model of culex quinquefasciatus, named Dynamic Mosquito Simulation Model (DyMSiM) that estimates population density using weather parameters, i.e. temperature and rainfall [17]. They used the concept of cumulative development in which each mosquito life cycle stage progresses only when the sum of development rates for each day exceeds 0.95 for egg, larva, and pupa stages, and 1.00 for adult stage. Considering the disastrous situation caused by dengue

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epidemics in recent decades, there is a dire need to develop a mathematical model that can imitate the reproductive behavior of Aedes mosquito based on regional and seasonal weather parameters (specifically temperature and rainfall) for Pakistan. To the best of our knowledge, no such model has been developed for Pakistan that takes into account the seasonal variation and de-termines the population trend of aedes mosquitoes.

After an analysis of the existing models and keeping in view their limitations, we have proposed a mathematical model that portrays dengue mosquito reproductive lifecycle and its population density (or concentration) under the influence of weather conditions. This study focusses on subtropical regions such as Pakistan, where weather conditions are ideal for dengue preval-ence. The model is developed using the concept of compartmental modelling, in which ae. Aegypti’s life cycle is divided into five compartments―egg, larva, pupa, pre-adult, and adult. The rate of change in the population of each of these compartments is calculated using Ordinary Differential Equations (ODEs). The birth, growth and death rates of the mosquito population vary with respect to the change in weather conditions i.e. temperature and rainfall. In this model, the development and mortality rates are calculated using temperature-based deterministic equations, where the daily mortality is also dependent on rainfall variation. The mathematical formulation is further implemented as a software simulation for visual analysis of aedes reproductive dynam-ics. The simulation model generates a temporal trend of dengue mosquito population with respect to the fluctuations in weather conditions. The results provides us with new insights focused on the impact of weather parameters on vector lifecycle. With the integration of temperature-dependent mortality rates, the effect of rainfall, and the use of compartmental dynamics, the repro -ductive behaviour of ae. Aegypti can be better understood by using our model. The independence of historical information on ae. Aegypti bionomics makes this model more flexible and adaptable to other subtropical regions.

II. METHODOLOGY

A. Geographical area under study

Located in the north of tropic of cancer, Pakistan is a sub-tropical country having ideal climatic conditions for dengue mos -quito reproduction during monsoon season. This study focuses on the urban area of Lahore city in Pakistan, situated at 31.5497° latitude and 74.3436° longitude. Weather parameters of the region, i.e. temperature and rainfall, are acquired from weather radars. For Lahore, the weather data shows seasonally repeated pattern throughout the year, starting with dry-cold at start of the year, dry-hot in mid-year, wet-warm during monsoon season, and finally dry-cold at the end of the year.

B. Reproductive mathematical model

In this research study, we categorize ae. Aegypti reproductive life cycle into five stages, namely egg, larva, pupa, pre-adult, and adult stage. The first stage begins with egg laying process (oviposition), in which an adult female ae. Aegypti lays eggs over a wet surface area––preferably near water containers (tyres, buckets, flowerpots etc.) [5]. The time required for egg incubation and hatching varies based on the availability of water and temperature conditions [6, 18]. The egg hatch process is followed by the larval stage––referred as the second stage of the reproductive lifecycle. The larva initially feeds on the food available inside the container, until it reaches a certain weight and size [5, 6]. When a minimum weight and size requirement is met, the larva begins hardening its body parts (metamorphosis), thus entering the third stage called the pupa stage [6]. Once the transformation of the pupa is complete, a mosquito emerges in pre-adult form. This stage is referred as the fourth stage of the reproductive cycle. In the pre-adult stage, the female mosquito, upon drying its wings, takes flight for mating, and feeds on blood to provide proteins necessary for egg development; this process is also known as the gonotrophic cycle [5]. After the gonotrophic cycle, the vector enters into the adult stage and is referred as the fifth and the final stage of the reproductive cycle, after which, the cycle repeats itself. The entire flow of ae. Aegypti life cycle described in this research study is illustrated in Figure 1.

Figure 1: Dengue mosquito reproductive model

To model the ae. Aegypti reproductive life cycle, we have applied the concept of compartment dynamics. In Figure 1, a com-partment (represented as a block) contains the population of a distinct stage while the ODE (represented as an arrow) varies the population of given compartment. The ODE’s are derived using the population of the previous compartment along with the pop-ulation, development and mortality rates of the current compartment.

The development rate for each stage is calculated using eq. 1 [7], where the parameter values of the equation for respective individual life cycle stage are shown in Table 1.

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RD (T )=RD (298K )( T

298 )× exp[( ∆ H A

1.987 )( 1298

− 1T )]

1+exp[( ∆ H H

1.987 )( 1T 1 /2

− 1T )]

(1)

Here, RD is the development rate at 298 K (diurnal), ΔHA and ΔHH are enthalpy changes (cal mol-1), T1/2 is the temperature (in Kelvin) at which half of the enzyme is active, and T is the daily temperature (in Kelvin).

Table 1: Parameter values for equation 1Stage RD

(298 K)ΔHA ΔHH T1/2 Refer.

Egg 0.24 10798 100000 14184 [16]Larva 0.20429 36072.78 59147.51 301.56 [6]Pupa 0.74423 19,246.42 5,954.35 302.68 [6]Adult 0.216 15725 1756481 447.2 [16]

Mortality rates (µ) are calculated using second order polynomial equation based on the variation of temperature [18]. For the entire aquatic phase (egg, larva and pupa) and female adult mosquitoes, the equations are defined as:

μ=0.54126−0.04458× T+0.00094 ×T 2 For 15 ≤ T ≤ 40 (2)

μ=0.1897−0.0133× T+0.0003 ×T 2 For 15 ≤ T ≤ 35 (3)

Here, T is the daily mean temperature (°C), eq. 2 represents the aquatic phase (egg, larva, and pupa), and eq. 3 represents the emerging female mosquitoes and adult infected mosquitoes. The population in the egg compartment increases with respect to the increasing number of adult mosquitoes of the previous compartment and decreases based on the development and mortality rates of the current egg population. The ODE for the egg population is shown in eq. 4.

dEdt

=EQ × A−RD E × E−μAQ × E (4)

Here, EQ represents the number of eggs laid by one female ae. Aegypti [5], A is the quantity of adult female ae. Aegypti, RDE

is the egg development rate, E is the egg population, and μAQ is the death rate of the aquatic phase as shown in eq. 2. The rate of change in larva population is based on the number of developed egg population from the previous compartment and the cur-rent development and mortality rates of the larval population, as shown in eq. 5.

dLdt

=RDE × E−RDL × L−μAQ × L (5)

Here, RDL is the larva development rate and L is the larva population. Similar to the larval ODE, the pupa population in-creases with respect to the number of developed larva from the previous population and decreases with respect to developed pupa population along with its daily mortality rate of the current population, as shown in eq. 6.

dPdt

=RDL × L−RDP × P−μAQ× P (6)

Here, RDP is pupa development rate, and P is the pupa population. According to [5], 45% of the pupa population emerge as female pre-adult mosquitoes. Therefore, the change in pre-adult stage varies with respect to developed female pupa from the previous stage, the rate of development and the daily mortality rates of the current stage as shown in eq. 7.

dPAdt

=0.45 × RD P× P−RD A × PA−μA × PA (7)

Here, RDA is adult development rate, PA is the pre-adult population, and μA is death rate for the adult stage [18]. The adult mosquitoes are responsible for transmitting dengue disease through blood feed. Eq. 8 represents the rate of change of adult pop-ulation with respect to pre-adult mosquitoes from the previous stage and the daily mortality rate of an adult mosquito (represen -ted as A).

dAdt

=RD A × PA−μA × A (8)

C. Simulation model

The proposed model is implemented as a system dynamics simulation model to analyse the reproductive lifecycle of dengue vector. System dynamics is based on the concept of stocks (i.e., the number of entities of the real system such as vectors and hu-mans) and flows (i.e., the rate of change of stock quantities from one stock to another). For our model, presented in Figure 2, we define the egg, larva, pupa, pre-adult, and adult compartments as stocks, while the rates (i.e. egg laying, egg hatching, larva de -velopment, pre-adult emergence, and gonotrophic cycle) are defined as flows. The simulation is initialized with the input para-

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meters (time and climatic-conditions) shown in Table 2. The model computes the diurnal vector density based on the reproduct-ive behavior shown in Figure 1, as explained in the previous section.

Table 2: Initial simulation parameters

ParameterSym-bol

Simulation paramet-ers

Egg population E 0Larva population L 0Pupa population P 0Pre-adult population PA 0Adult population A ≥ 1Min. water threshold - ≥ 20 cmTemperature T Weather Lahore 2011Rainfall - Weather Lahore 2011Egg quantity EQ 83

Figure 2 - Reproductive simulation model

III. RESULTS

The climatic variations of Lahore city for the years 2011 to 2014 is presented in Figure 3. The figure shows maximum/mini-mum temperature and rainfall distributions throughout the year along with temperature thresholds suitable for adult mosquito survival. As shown in the figure, the trend of temperature remains the same annually while rainfall incidence varies for each year. At the beginning of the year, the temperature gradually rises, becoming optimal from March to May to initiate mosquito reproduction (i.e. temperature in the range from 15°C to 35°C). However, due to low frequency of rainfall ( i.e. weekly average less than 20mm) we expect low mosquito reproduction rate in these months. Even though the rainfall incidence is high in the later months of June and July, but rise in temperature beyond adult mosquito maximum threshold (i.e. greater than 35°C) causes a decline in mosquito survivability. Alternatively, in August the increase in rainfall and decrease in temperature causes a corre -sponding rise in the mosquito population. Later on, the adult mosquito reproduction decreases gradually until early November due to decrease in temperature and rainfall. The cycle repeats itself for subsequent years as per the given conditions.

Figure 3 - Climatic Trend of Lahore, year 2011 - 2014

Simulation results representing the population dynamics of egg, larva, and pupa for the year 2011 are shown in Figure 4 to Figure 6, respectively. Figure 7 to Figure 10 represent the final population trend of adult female aedes aegypti obtained from our simulation model for the year 2011 to 2014, respectively. In the year 2011 as shown in Figure 7, due to lack of water avail -ability for the months prior to May, our model did not simulate a rise in mosquito population. With the steady decrease in tem -perature and increase in rainfall in the following month, the simulation revealed a slight increase in egg population in mid-June as shown in Figure 4. This increase in egg population leads to a corresponding increase in adult mosquito population in late-June as shown in Figure 7. Likewise, from late-July to early August, the survival rates of egg, larva, and pupa population in-

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creased considerably owing to ideal weather conditions, causing an increase in female mosquito population. After the peak ob -served in late-July, the simulation results show a sharp decrease in mosquito reproduction in early August, as shown in Figure 6. This resulted in corresponding decrease in female mosquito population in later months, where the mortality rate was based on aedes aegypti life span.

Figure 4: Normalized egg population, June - October 2011 Figure 5: Normalized larva population, June - October 2011

Figure 6: Normalized pupa population, June - October 2011 Figure 7 - Normalized female adult population, year 2011

Figure 8 - Normalized female adult population, year 2012 Figure 9 - Normalized female adult population, year 2013

Figure 10 - Normalized female adult population, year 2014

IV. DISCUSSION

This study aims to develop a model that can determine the temporal trend of aedes aegypti population based on the variation of temperature and rainfall. In this study, we formulated a generic mathematical model followed by its implementation in the form of a simulation model.

Climate in Lahore city is classified into six major climatic zones i.e. dry-cold, wet-cold, dry-warm, wet-warm, dry-hot, and wet-hot, as shown in Table 3. In the Table, dry and wet represents water availability while cold, warm, and hot represents op-timal and extreme temperature conditions. For the region under study, rainfall generally occurs during the months of February and April followed by the monsoon season from July to September. For the rest of the months, the region experiences either dry climatic or extreme temperature conditions.

Our simulation results revealed that mosquito reproduction is highly dependent on rainfall and temperature. Early stages of the mosquito life cycle (i.e. egg hatching, larval growth) do not progress until temperature is in the range from 15°C to 40°C provided sufficient water is available. For instance, in Figure 5, we observe a rise in the larval population in early-July and late August, however, corresponding rise in pupa population was not observed (Figure 6), as larva could not survive due to insuffi-cient water quantity. On the other hand, as shown in Figure 7 during the month of June, although rainfall was sufficient, yet mosquito population did not rise until the start of July because temperature was above our maximum optimal threshold ( i.e. 40°C). We have classified the mosquito reproduction based on weather conditions into three categories: no reproduction (in dry-

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cold and dry-hot months), low mosquito reproduction (in dry-warm and wet-hot months), and peak reproduction (in wet-warm months).

Table 3 - Climatic Zones of Lahore averaged for year 2011 - 2014

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Climate Zone

DryCold

Wet Cold

Dry Warm

Wet Warm

Dry Hot

Wet Hot

Wet Warm

Wet Warm

Wet Warm

Dry Warm

Dry Cold

Dry Cold

Avg. High Temp (°C)

17.7 20.5 27.1 33.2 39.1 39.7 36.2 34.2 33.6 31.8 27.0 20.5

Mean Temp (°C)

12.1 14.9 20.9 26.4 32.1 33.6 31.4 30.0 29.3 26.1 20.2 14.2

Avg. Low Temp (°C)

6.5 9.3 14.6 19.6 25.1 27.4 26.5 25.9 24.9 20.5 13.4 7.8

Avg. Rain (mm)

9.0 32.2 17.1 32.2 11.7 88 142 215.2 208.6 12.7 8.5 5.3

The impact of weather parameters on the aedes population has been observed in several previous studies [5, 6, 12, 13, 14, 15,18]. Our simulation results coincide with the results presented by these previous models and show the importance of temperat-ure and rainfall on the mosquito reproduction. Morin et al. describe a substantial increase in population during spring due to considerable increase in precipitation and temperature [17]. It correlates to the wet-warm climatic zone of our region in April (late spring), where average rainfall is greater than 30 mm, and temperature is in the range from 15 °C to 35 °C. During sum-mer, the population trend presented by Morin et al. declined due to high temperature and low precipitation. Similar results were found for our region, where the mosquito reproduction significantly decreased in May due to dry-hot climatic conditions. Hopp et al. made comparable observations stating that the density of mosquito population increases in warm months (wet-warm cli -mate) and decreases in cold months (dry-cold climate) [14].

According to Rueda et al., the survival rate of aedes aegypti from egg to adult stage varies with respect to temperature vari-ation. They have calculated the survival rate to be approximately 3% at temperature below 15 °C, 90% at optimal temperature of 27 °C and 59% at temperature of 34 °C [6]. In accordance with Rueda et al., we define the daily mortality rate as a function of temperature (refer to eq. 2 and 3) to capture the variation in the population of each life cycle stage. It is an improvement to the previously developed models [12, 14], as in these studies the survival rate of aedes aegypti are linearly approximated. Table4 represents survival rates of aedes aegypti at varying temperatures compared with other studies. For adult mosquito in our model, we observe an increase in survival rate until optimal temperature of 25 °C, after which the survival rates decrease. Com-paratively, Hopp et al. [14] represent 100% survival from 5 °C to 34 °C while Otero et al. [15] considered adult mosquito sur-vival to be independent of temperature. This denotes that the survival rate used in our model varies in relation to temperature changes while in previous studies the variation in temperature is considered to have negligible effect.

Table 4 - Survival rates of aedes aegypti at varying temperatures

Temperat-ure

Our Model Hopp et al. Otero et al.

Larva Adult Larva AdultLarv

aAdult

5 °C 5 % 5 % 0 % 100 % 0 %

91 %

15 °C 92 % 94 % 100 % 100 % 96 %20 °C 97 % 96 % 100 % 100 % 99 %25 °C 99 % 96 % 100 % 100 % 99 %27 °C 98 % 95 % 100 % 100 % 99 %30 °C 95 % 94 % 100 % 100 % 99 %34 °C 89 % 92 % 100 % 100 % - -40 °C 74 % 5 % 100 % 0 % - -44 °C 5 % 5 % 0 % 0 % - -

Otero et al. neglected the influence of rainfall on the overall reproductive process, since for their local environment it rains throughout the year on regular basis, thus eliminating the need of water for aedes mosquito reproduction. In their study, they used a deterministic equation to calculate the mean daily temperature; instead, we used actual weather conditions obtained from local weather stations. With their regional annual temperature ranging from 10 °C to 25 °C, the simulation results presented by Otero et al. illustrate a periodic trend of mosquito population for each year that varies solely due to the variation in temperature. From their results, a sharp rise in mosquito population is observed in spring showing peak reproduction in mid-summer, fol -lowed by a monotonic decrease in autumn and finally stops in winter. Comparing with our results, we do not observe a sharp rise in spring (March and April); instead, we observe a slight variation in the mosquito population as shown in Figure 10. The cause of this phenomenon is the lack of rainfall in our region under study. The difference in the results discloses that for our re-gion, rainfall is an essential input parameter and has a dominant role in depicting the reproductive behaviour of aedes mosqui-toes.

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For validation purpose, simulation results were correlated with the number of infected dengue patients reported at various hospitals in Lahore city over the same timeline. According to Figure 7, the infected dengue patients begin to emerge in late-July, whereas the first peak of mosquito population was observed in late-June. Correspondingly, the second mosquito population peak was observed at the beginning of August while actual recorded dengue patients were observed at the end of the respective month. Dominant factors responsible for this latency include virus incubation time (time needed for virus replication) and time consumed in laboratory tests for confirmation of the virus in a patient.

Several assumptions made were considered to have negligible effect on the overall reproductive process of aedes aegypti. For instance, we assumed that the temperature of the water container with larva residing inside is equal to the mean daily temperat-ure obtained from weather stations [14]. We also assume that the influence of predation, food availability for larva and adults, and human involvement have a negligible effect on the overall reproductive process [14, 15]. Furthermore, aedes aegypti was considered the only mosquito that reproduces in a given breeding site, the possibility of another mosquito reproducing in the same breeding site was not accounted for in our model.

While the dominant factors, i.e. temperature and rainfall explain much of the seasonal fluctuations in the reproductive beha-vior, several socioeconomic or socio-ecological factors limit the accurate analysis of emerging aedes mosquito population. For instance, Morin et al. present three different land cover types that contribute to the quantity of available water for mosquito re-production i.e. permeable, non-permeable and permanent water resources [17]. Whereas in our model, rainfall is the only source of water––water sources such as domestic storage tanks and irrigation were not considered. Public education and mosquito erad-ication program significantly affect aedes mosquito population. In 2012, Punjab government performed large-scale dengue sur-veillance and eradication program that significantly decreased the population density of larvae, resulting in decreased infection rate. In the Figure 8, we observe a peak reproduction time in mid-September, yet no peak of emerging patients in the following month was observed.

Considering these limitations, our model can efficiently simulate the change in mosquito population based solely on the vari-ation in weather parameters. The developed model can also find its application in other subtropical regions, provided the weather parameters are available. Using our simulation results, we can identify an optimal time zone when counter measures will have the highest impact on mosquito reproduction, as a result decreasing the number of emerging infected patients.

V. CONCLUSION

In this research, we have derived a mathematical model that portrays aedes aegypti reproductive life cycle. We achieved this by using ODE via the concept of compartmental modelling. Through our simulation using system dynamics, we showed how temperature and rainfall are essential parameters for aedes mosquito reproduction and play a dominant role in seasonal fluctu-ations of mosquito population in subtropical regions such as Lahore. Using weather data, we can delineate the time zones re -sponsible for aedes reproduction and dengue outbreaks. From our results, we found that ae. Aegypti reproduction is lowest dur-ing winter and summer seasons, moderate in late spring and highest during monsoon season.

The model has several applications: 1) it is useful in locations where mosquito surveillance is a challenging task; 2) the con -cepts behind our model using ODEs are applicable to other mosquito species; 3) it can provide new insights for strategic de -cision-making and planning, and devising effective countermeasures against future dengue outbreaks. Aedes aegypti is also re-sponsible for Yellow fever and Chikungunya virus; hence, the simulation results are not only limited to dengue. Our developed simulation model is being used at Centre for System Simulation and Visual Analytics Research (C-SVAR), University of Engin-eering and Technology, Lahore, as an asset for a variety of dengue epidemic related studies.

The model developed in this research can be further improved by varying the survival (or mortality) rates through the implic -ation of socioeconomic factors such as mosquito eradication programs and public awareness. Integrating the transmission beha -vior of human-vector interaction, this model will be useful in forecasting infected dengue patients in a given region.

ACKNOWLEDGMENT

We are grateful to Centre for System Simulation and Visual Analytics Research (C-SVAR) for providing us with the research op-portunity. We also appreciate the support of National ICT R&D Fund for funding this research.

REFERENCES

[1] S. Bhatt, P. W. Gething, O. J. Brady and J. P. e. a. Messina, "The global distribution and burden of dengue," Nature, vol. 496, p. 504–507, April 2013.

[2] J. Orozco, "Defeating dengue: a difficult task ahead," Bull World Health Organization, vol. 85, no. 10, pp. 737-738, October 2007.

[3] M. R. Khanani, A. Arif and R. Shaikh, "Dengue in Pakistan: Journey from a Disease free to a Hyper Endemic Nation," Journal of the Dow University of Health Sciences Karachi, vol. 5, no. 3, pp. 81-84, 2011.

[4] P. I. T. Board, "Epidemics Prevention and Control Program," Health Department, Government of Punjab, 9 December 2014. [Online]. Available: http://health.punjab.gov.pk/?q=EPCP. [Accessed 4 June 2015].

[5] S. R. Christophers, Aedes Aegypti (L.): The Yellow Fever Mosquito, London: Cambridge University Press, 1960.[6] L. M. Rueda, K. J. Patel, R. C. Axtell and R. E. Stinner, "Temperature-Dependent Development and Survival Rates of

Culex quinquefasciatus and Aedes aegypti (Diptera: Culicidae)," Journal of Medical Entomology, vol. 27, no. 5, pp. 892-898, 1990.

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[7] R. Schoolfield, P. Sharpe and C. Magnuson, "Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory," Journal of Theoretical Biology, vol. 88, no. 4, pp. 719-731, February 1981.

[8] D. A. Focks, E. Daniels, D. G. Haile and J. E. Keesling, "A simulation model of the epidemiology of urban dengue fever: Literature analysis, model development, preliminary validation, and sample of simulation results," The American Journal of Tropical Medicine and Hygiene, vol. 53, no. 5, pp. 489-506, 1995.

[9] S. Hales, N. d. Wet, J. Maindonald and A. Woodward, "Potential effect of population and climate changes on global distribution of dengue fever: an empirical model," THE LANCET, vol. 360, pp. 830-34, September 2002.

[10] M. Derouich, A. Boutayeb and E. H. Twizell, "A model of dengue fever," BioMedical Engineering OnLine, vol. 2, no. 4, 2003.

[11] J. Helmersson, "Mathematical Modeling of Dengue -Temperature Effect on Vectorial Capacity," 2012.[12] D. A. Focks, D. G. Haile, E. Daniels and E. A. Mount, "Dynamic life table model for Aedes aegypti (Diptera: Culicidae):

Analysis of the literature and model development.," Journal of Medical Entomology, vol. 30, no. 6, pp. 1003-17, November 1993.

[13] D. A. Focks, D. G. Haile, E. Daniels and G. A. Mount, "Dynamic Life Table Model for Aedes Aegypti (Dipetera: Culcidae): Simulation Results and Validation," Medical and Veterinary Entomology Research Laboratory , vol. 30, no. 6, pp. 1018-1028, 1993.

[14] M. J. HOPP and J. A. FOLEY, "Global-Scale Relationships between Climate and the Dengue Fever Vector, Aedes Aegypti," Climate Change, vol. 48, no. 2-3, pp. 441-463, 2001.

[15] M. Oteroa, H. G. Solari and N. Schweigmann, "A Stochastic Population Dynamics Model for Aedes Aegypti: Formulation and Application to a City with Temperate Climate," Bulletin of Mathematical Biology, vol. 68, pp. 1945-1974, July 2006.

[16] M. Oteroa, N. Schweigmann and H. G. Solaria, "A Stochastic Spatial Dynamical Model for Aedes Aegypti," Bulletin of Mathematical Biology, vol. 70, no. 5, pp. 1297-1325, 2008.

[17] C. W. Morin and A. C. Comrie, "Modeled response of the West Nile virus vector Culex quinquefasciatus to changing climate using the dynamic mosquito simulation model," International Journal of Biometeorology, vol. 54, no. 5, pp. 517-529, August 2010.

[18] H. M. Yang, M. L. G. Macoris, K. C. Galvani, M. T. M. Andrighetti and D. M. V. Wanderley, "Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue," Epidemiology and Infection, vol. 137, no. 8, pp. 1188-1202, August 2009.

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