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M O D E L I N G D E N G U E T R A N S M I S S I O N I N I N D O N E S I A B Y

I N T E G R A T I N G T E M P E R A T U R E - D E P E N D E N T M O S Q U I T O

B E H A V I O R U S I N G T H E S I R - S I M O D E L

N U R U L A T I Q A H A Y U N I B I N T I Z U L K I F L I ( K 2 4 2 / 6 0 )

S U P E R V I S O R : P N . R A H A I D A H B I N T I M U H A M M A D

ABSTRACT

Aedes The mathematical model SIR-SI has evaluated the influence of temperature on dengue transmission dynamics quite carefully

in Indonesia under various recent conditions. The research aimed quite deliberately to develop the SIR-SI model and calculate

aegypti with many basic reproduction numbers R0 amidst various temperature changes on transmission dynamics. The model

mosquito effectively combines human population through Susceptible-Recovered dynamics and mosquito population through

Susceptible-Infected dynamics. The key parameters were modified at different temperatures of 15 °C, 28 °C and 40 °C which

correspond to biological changes that are quite dependent on temperature fluctuations. The eigenvalues of the Jacobian

matrix were examined to find the equilibrium point and evaluate the stability quite carefully in the meantime. The results

showed that R0 peaked at 28 °C around 0.088 representing ideal conditions for mosquito activity and virus replication and

decreased sharply at 15 °C and 40 °C due to increased mortality. Disease-free equilibrium stays stable across tested

temperatures with R0 less than 1 thereby indicating persistence under varied environmental conditions somehow. Research

findings indicate temperature significantly influences dengue transmission risk thereby underscoring need for factoring

environmental elements into diverse prevention strategies nowadays effectively. Further meteorological variables and local

data incorporation yields substantially more accurate forecasts and quite effective vector management strategies

successfully.

PROBLEM STATEMENT IMPLEMENTATION

i) DISEASE FREE Equilibrium point (DFEP) iii) Basic Reproduction Number,R0

Dengue threatens over half the world’s population. Existing models often

ignore how temperature affects mosquito behavior and virus transmission,

compromising prediction accuracy. This study addresses this gap by

incorporating temperature-dependent mosquito behavior into an SIR-SI

model to improve predictions and intervention strategies in Indonesia.

ii) Stability Analysis of the Equilibrium Points

OBJECTIVES

1. To formulate the SIR-SI model and calculate the basic reproduction

number. R0 is less than one, implying that the points

2. To analyse the effect of different temperature (minimum, average, defined by the disease-free equilibrium

Since all the roots of eigenvalues are point (DFEP) will be locally asymptotic stable.
maximum) on dengue transmission using SIR-SI model.

negative, so the system is stable.

METHODOLOGY RESULTS & DISCUSSION

i) MODEL FORMULATION

iv) Stability Analysis of the Equilibrium Points

The simulation results indicate that temperature

significantly affects dengue transmission

dynamics. At 15°C, mosquito activity and virus

replication are low, resulting in minimal

transmission potential (R0=0.0128). At 28°C,

conditions are optimal for mosquito survival and

viral replication, giving the highest transmission

potential (R0=0.0880). At 40°C, despite increased

mosquito activity, high mortality rates reduce

overall transmission (R0=0.0752). Across all

ii) Equilibrium points temperatures, R0<1, suggesting that the disease-
v) Basic Reproduction Number,R0 free equilibrium remains stable, and the risk of a

large-scale outbreak under these parameters is

low.

CONCLUSION RECOMMENDATION

This study shows that temperature plays a crucial role in dengue

transmission by affecting mosquito survival, biting rates, and virus Future studies should incorporate local meteorological

iii) DISEASE FREE Equilibrium point (DFEP), replication inside the mosquito. Using the SIR-SI model, we found that data and other environmental factors such as humidity and

Ih=Iv=0 transmission risk is highest at around 28°C, where mosquito and virus rainfall to improve the model’s accuracy. Collecting more

activity are optimal. At 15°C, low temperatures slow mosquito behavior field data on mosquito and human behavior in specific

and virus growth, leading to minimal transmission risk. At 40°C, regions of Indonesia will help refine the parameters and

although mosquito activity initially increases, high mortality from heat make predictions more reliable. This approach can support

stress reduces the overall risk. Since R0<1 in all scenarios, the more effective and targeted dengue prevention and control

disease-free equilibrium remains stable, suggesting that under strategies.

current conditions, a major outbreak is unlikely.