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STABILITY ANALYSIS ON MATHEMATICAL MODEL OF

RECRUDESCENCE OF MALARIA IN INDONESIA

NAME: INTAN NOOR LIANA BINTI SUPERVISOR’S NAME: MADAM NURUL

ZAKARIA (K242/32) AKMA MOHAMAD RASAT

ABSTRACT

Malaria is still a serious health problem in many tropical countries, including Indonesia. One big challenge is recrudescence, where

the disease comes back after treatment because the parasite is not fully gone. This study uses a SELITR model that divides people

into six groups: Susceptible, Exposed, Latent, Infectious, Treated, and Recovered. It helps to understand how malaria spreads and

why it stays in the population. The model looks at important things like treatment failure, losing immunity, and moving between

stages of the disease. A stability test using a mathematical method was done to study two situations: when malaria goes away

(disease-free) and when it stays at a low level (endemic). The results show that malaria can be eliminated, but relapse and re-

infection make it harder. This means good treatment, strong health action, and regular check-ups are needed to stop malaria from

coming back. The results can help improve future plans to control and remove malaria in Indonesia and other affected places.

PROBLEM STATEMENT METHODOLOGY

Malaria is still a big problem in Sub-Saharan Africa. The disease

often comes back after treatment because the parasite isn’t fully MODEL FORMULATION

gone. This is called recrudescence. It happens due to wrong

medicine use, fake drugs, or weak immune systems. Hot weather

and poor healthcare also make things worse. There are still not

enough studies on recrudescence, and some model parts need to

change to test treatment better. Understanding this can help

improve malaria control and save more lives.

OBJECTIVE

To construct SELITR Model of Malaria transmission with EQUILIBRIUM POINT

recrudescence in human population.

To investigate the stability analysis of disease-free equilibrium

point and endemic equilibrium point for malaria transmission.

IMPLEMENTATION

DFEP EEP

STABILITY ANALYSIS

BASIC REPRODUCTION NUMBER

CONCLUSION & RECOMMENDATION

The study concludes that malaria can be

controlled if the basic reproduction number R0 is

less than 1. However, recrudescence increases the

risk of the disease returning, making elimination

more challenging. Stability analysis shows that

complete treatment and strong control measures

RESULT & DISCUSSION are important to stop the spread and reduce

relapse. It is recommended to improve malaria

The model shows two main outcomes: disease-free equilibrium (DFE), treatment quality and ensure patients complete

where malaria disappears, and endemic equilibrium (EEP), where it the full course of medication to prevent

stays at a low level. The basic reproduction number R0 plays a key role recrudescence. Health authorities should

if R0 < 1, malaria will die out; if R0 > 1, it can spread. Stability analysis strengthen monitoring and follow-up systems to

using the Jacobian matrix confirms that DFE is stable when all detect and manage relapse cases early. Public

eigenvalues are negative. The recrudescence parameter κ2 , which awareness about the importance of completing

represents treatment failure, increases the chance of relapse and treatment must also be increased. Lastly, further

makes elimination harder. These results highlight the need for effective studies should explore how changes in treatment

treatment and careful monitoring to reduce the impact of malaria in the failure rates affect malaria spread, to support

population. better health strategies in Indonesia.