SEIR1R2 Mathematical Model for Plasmodium falciparum Recrudescence in Indonesia

Fitri Cahyani; Akhmad Sultoni; Luffy Ardiansyah; Anisa Arnaz; Sofan Irawan; Solikhatun Solikhatun

doi:10.22342/jims.v32i4.2029

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Fitri Cahyani ⁽¹⁾ , Akhmad Sultoni ⁽²⁾ , Luffy Ardiansyah ⁽³⁾ , Anisa Arnaz ⁽⁴⁾ , Sofan Irawan ⁽⁵⁾ , Solikhatun Solikhatun ⁽⁶⁾

(1) Department of Mathematics, Universitas Gadjah Mada, Indonesia,

(2) Department of Mathematics, Universitas Gadjah Mada, Indonesia,

(3) Department of Mathematics, Universitas Gadjah Mada, Indonesia,

(4) Department of Mathematics, Universitas Gadjah Mada, Indonesia,

(5) Department of Mathematics, Universitas Gadjah Mada, Indonesia,

(6) Department of Mathematics, Universitas Gadjah Mada, Indonesia

https://doi.org/10.22342/jims.v32i4.2029

Issue
Vol. 32 No. 4 (2026): December

Keywords:

Malaria, Mathematical model, Recrudescence, Plasmodium falciparum, Equilibrium analysis

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Abstract

Malaria remains one of the most challenging infectious diseases to eradicate, with a high prevalence in tropical regions, particularly in Indonesia, where \textit{Plasmodium falciparum} accounts for a substantial proportion of reported cases. This study develops a compartmental mathematical model to analyze malaria transmission dynamics in human populations by incorporating both recrudescence and reinfection processes. The proposed model extends the classical SEIR framework by introducing two additional compartments: $R_1$, representing individuals at risk of recurrence due to incomplete parasite clearance, and $R_2$, representing individuals who have fully recovered but remain susceptible to reinfection. The model is formulated as a system of five nonlinear ordinary differential equations. The basic reproduction number, $R_0$, is derived using the Next Generation Matrix method, and the stability of both the disease-free and endemic equilibrium points is examined through local stability analysis and the Routh--Hurwitz criteria. Numerical simulations are conducted to illustrate the dynamic behavior of the system under various parameter settings. The results highlight the influence of treatment, recovery, and transmission parameters on disease persistence or elimination, providing a mathematical foundation for further epidemiological analysis and the development of control strategies.

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