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Sains Malaysiana 53(12)(2024): 3425-3435
http://doi.org/10.17576/jsm-2024-5312-23
A Compartmental
Model for the Transmission Dynamics of Rabies Disease in Dog Population
(Suatu Model Petak untuk Transmisi Dinamik Penyakit Rabies dalam Populasi Anjing)
THANISHA
KALIAPAN1, NYUK SIAN CHONG1,2,*, ILYANI ABDULLAH1,2,
ZABIDIN SALLEH1,2 & JANE LABADIN3
1Faculty of Computer Science and
Mathematics, Universiti Malaysia Terengganu, 21030
Kuala Nerus, Terengganu, Malaysia
Received: 6
February 2024/Accepted: 21 October 2024
Abstract
Dogs are
the main source of more than 90% of human rabies infections that pose a
significant threat to public health, primarily in Africa and Asia. However, it
is also one of the viral diseases that can be prevented by vaccination that
affects both warm-blooded animals and humans. There are two types of rabies
vaccines: pre-exposure prophylaxis and post-exposure prophylaxis (PEP). Mathematical models can be valuable tools for
predicting and controlling the spread of rabies disease. Thus, we introduce an
SEIV (Susceptible-Exposed-Infected-Vaccinated) model incorporate vaccination
control strategy to examine the transmission dynamics of rabies disease in dog
population. The basic reproduction number, , positively invariant and attracting region,
steady states, and the stability analysis of the model are investigated. We
find that there are two equilibria exist in the model, i.e., disease-free and
endemic equilibria. To prove the global stability of disease-free and endemic
equilibria, the theory of asymptotic autonomous system and geometric approach
have been applied, respectively. Hence, we find that the disease-free and
endemic equilibria are globally asymptotically stable if and , respectively. Numerical
simulations are performed to depict the dynamics of the model. As a conclusion,
we will be able to control the disease effectively if the vaccination rate is
sufficiently large.
Keywords:
Nonlinear ordinary differential equation; numerical simulation; rabies disease;
stability analysis; steady state
Abstrak
Anjing merupakan punca utama lebih daripada 90% jangkitan rabies manusia yang menimbulkan ancaman ketara kepada kesihatan awam, terutamanya di Afrika
dan Asia. Walau bagaimanapun, ia juga merupakan salah satu penyakit virus yang boleh dicegah dengan vaksinasi yang memberi kesan kepada haiwan berdarah panas dan manusia. Terdapat dua jenis vaksin rabies: profilaksis pra-pendedahan dan profilaksis pasca-pendedahan (PPP). Model matematik boleh menjadi alat yang berguna untuk meramal dan mengawal penyebaran penyakit rabies. Oleh itu, kami memperkenalkan suatu model SEIV (Rentan-Terdedah-Dijangkiti-Diberi vaksin)
yang menggabungkan strategi kawalan vaksinasi untuk mengkaji dinamik penularan penyakit rabies dalam populasi anjing. Nombor reproduksi asas, , rantau invarian positif dan menarik, keadaan pegun dan analisis kestabilan model telah dikaji. Kami mendapati bahawa terdapat dua titik keseimbangan yang wujud dalam model, iaitu, titik keseimbangan bebas penyakit dan endemik. Untuk membuktikan kestabilan global bagi titik keseimbangan bebas penyakit dan endemik, teori sistem autonomi asimptotik dan pendekatan geometri masing-masing telah diaplikasi. Oleh itu, kami mendapati bahawa titik keseimbangan bebas penyakit dan endemik masing-masing mencapai kestabilan secara asimptotik secara global jika dan . Simulasi berangka dijalankan untuk menggambarkan kedinamikan model. Kesimpulannya, kita akan dapat mengawal penyakit ini dengan berkesan sekiranya kadar vaksinasi cukup besar.
Kata kunci: Analisis kestabilan; keadaan pegun; penyakit rabies; persamaan pembezaan biasa tak linear; simulasi berangka
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