Page 32 - POSTER FYP MAC-OGOS 2025

SEIR MODEL OF THE MALARIA REINFECTIONS

IN HUMAN POPULATIONS IN INDONESIA

Prepared by : Najihah Masrurah Bt Wali

Supervisor : Puan Nurul Akma Bt Mohamad Rasat K242/33

ABSTRACT

Malaria remains a major health problem in Indonesia, especially in high-risk areas like Papua and East Nusa Tenggara. One challenge in

controlling malaria is reinfection, where a recovered person gets infected again through another mosquito bite. This study developed an

SEIR model with reinfection using Maple software and real data to explore how reinfection affects malaria spread. The results showed a

basic reproduction number (R₀) of 0.0771, suggesting the disease is unlikely to cause an outbreak and that the disease-free state is

stable. However, some results in the endemic state were unrealistic, possibly due to data or model limitations. This highlights the

importance of including reinfection in malaria studies and the need for further research with better data and improved models.

PROBLEM STATEMENT

Reinfection is becoming a rising public health concern in malaria, especially in areas METHODOLOGY The Model

with high transmission and low long-term immunity. While past studies have used SEIR

or SEIRS models to understand malaria dynamics, many have not focused on reinfection

specifically. For example, Maulana and Ramdani (2024) used an SEIRS model and found Formulation ODE of the Model

a low basic reproduction number (R₀), suggesting malaria would not reach epidemic

levels but they did not directly study the reinfection process. This creates a research

gap in understanding how repeated exposure, treatment, and temporary immunity

contribute to reinfection. To address this, our study uses an SEIR model built in Maple,

designed to focus on reinfection and its effect on malaria control and persistence. Endemic Equilibrium

OBJECTIVE

To formulate SEIR model for malaria reinfections in human

populations.

To perform stability analysis on the disease-free equilibrium point Disease-free Equilibrium

and endemic equilibrium point for malaria transmission dynamic.

IMPLEMENTATION

Disease-free Equilibrium, E=I=0 Endemic Equilibrium,

I not equal 0

Basic Reproduction Number

Stability Analysis, DFE Stability Analysis, EE

Basic Reproduction Number Stability Analysis, DFE

Stability Analysis, EE

RESULT & DISCUSSION

SEIR Model Simulation

The SEIR simulation showed typical epidemic

behavior. At the start, the susceptible population was

high but quickly dropped as people were exposed to

infection. The exposed and infected groups increased

rapidly in the early days, then sharply declined, with

infections nearing zero within 10 days. Recoveries

peaked at over 130,000 within the first five days, then

gradually decreased from around day 30 to day 120.

This pattern reflects a fast, intense outbreak followed

by a slow and steady recovery phase.
CONCLUSION & RECOMMENDATION

Basic Reproduction Number This study aimed to develop and analyze an SEIR model to understand malaria

reinfections in Indonesia, using parameters from Maulana and Ramdani (2024) and

Discussion: Since R0 < 1, the disease-free

equilibrium is locally asymptotically simulated with Maple software. The model tracked the dynamics of susceptible,

stable, and so malaria won’t result in an exposed, infected, and recovered populations, showing typical epidemic patterns.

outbreak if nothing changes Reinfection was represented through loss of immunity, causing a gradual decline in

the susceptible group. The basic reproduction number (R₀) was 0.0771, indicating a

Stability Analysis

stable disease-free state and low risk of outbreak. However, the endemic scenario

Discussion: All eigenvalues at DFE are negative from the simulation, which showed unrealistic negative values, likely due to data or model limitations. To improve

guarantees the disease-free equilibrium’s local stability. For endemic equilibrium accuracy, future research should use real-time data, include mosquito dynamics, and

(EEP), having a negative susceptible value guarantees that the EEP is not extend the model to SEIRS to reflect temporary immunity. Effective treatment and

possible biologically in the long-term prediction. This could be due to

overestimated recovery or reinfection rates targeted public health strategies remain essential for controlling malaria reinfection

and spread.