Assessing Control Strategies for Monkeypox: A Compartmental Model Including Vaccinated, Quarantined, and Hospitalized Individuals

Öz

Monkeypox is an infectious disease originating in animals, caused by a double-stranded DNA virus. It spreads between humans through close contact with infected persons or animals, especially during intimate interaction and via respiratory secretions. Because its symptoms resemble other viral diseases, diagnosis is difficult and requires laboratory confirmation. With increasing infection rates, particularly in resource-limited countries, monkeypox has become a growing global health concern, emphasizing the need for effective prevention and control. In epidemiology, mathematical modelling is essential for understanding disease spread, predicting outbreaks, and evaluating control strategies. These models provide insights into transmission patterns and are used to assess interventions such as vaccination, isolation, and hospitalization. This study introduces a new compartmental model, SVEIQHR, designed to examine the combined effects of quarantine and vaccination on monkeypox transmission. The model divides the population into seven groups: Susceptible, Vaccinated, Exposed, Infectious, Quarantined, Hospitalized, and Recovered. Unlike previous studies analyzing these components separately, this integrated model provides a more comprehensive representation of disease control mechanisms and evaluates multiple interventions within one framework. Mathematical techniques, including the next-generation matrix, were applied to determine the basic reproduction number, as well as the disease-free and endemic equilibrium points. Stability was assessed using eigenvalue-based methods. Numerical simulations with the Runge–Kutta method illustrate the model’s dynamics across various time intervals through tables and visual plots. This framework contributes to understanding monkeypox transmission and control. Future work will refine the model by adding subgroups such as asymptomatic, pre-symptomatic, and treated individuals.

Anahtar Kelimeler

• Monkeypox modelling
• Vaccination impact
• Quarantine strategy
• Hospitalization effect
• Stability analysis

Maymun Çiçeği İçin Kontrol Stratejilerinin Değerlendirilmesi: Aşılanmış, Karantinaya Alınmış ve Hastaneye Yatmış Bireyleri İçeren Bölmeli Bir Model

Öz

Maymun çiçeği hastalığı, hayvan kökenli bir enfeksiyon olup çift sarmallı DNA virüsü tarafından oluşturulur. Enfekte kişilerle veya hayvanlarla yakın temas, özellikle fiziksel veya cinsel temas ve solunum salgıları yoluyla insandan insana bulaşır. Belirtileri diğer viral hastalıklarla benzerlik gösterdiğinden tanı zor olup laboratuvar doğrulaması gerektirir. Enfeksiyon oranlarının özellikle kaynakları sınırlı ülkelerde artmasıyla, maymun çiçeği küresel bir sağlık sorunu haline gelmiş ve etkili önleme ile kontrol önlemlerine duyulan ihtiyacı artırmıştır. Epidemiyolojide matematiksel modelleme, hastalıkların yayılımını anlamada, salgınları tahmin etmede ve kontrol stratejilerini değerlendirmede temel bir araçtır. Bu modeller, bulaşma dinamikleri hakkında önemli bilgiler sunar ve aşılama, izolasyon ve hastaneye yatırma gibi müdahalelerin etkinliğini değerlendirmede kullanılır. Bu çalışma, karantina ve aşılama stratejilerinin birlikte etkisini incelemek için geliştirilen yeni bir bölmeli modeli, SVEIQHR modelini sunmaktadır. Model, nüfusu yedi gruba ayırır: Duyarlı, Aşılı, Maruz, Bulaşıcı, Karantinaya Alınmış, Hastanede Yatan ve İyileşmiş. Önceki çalışmalarda bu unsurlar ayrı ayrı incelenirken, bu entegre model hastalık kontrol mekanizmalarını daha bütüncül biçimde temsil eder ve birden fazla müdahaleyi aynı çerçevede değerlendirir. Matematiksel analizlerde yeni nesil matris yöntemi kullanılarak temel üreme sayısı ve hastalıksız ile endemik denge noktaları belirlenmiştir. Dengenin kararlılığı özdeğer tabanlı yöntemlerle incelenmiştir. Runge–Kutta yöntemi ile yapılan sayısal simülasyonlar, farklı zaman aralıklarında modelin dinamiklerini tablo ve grafiklerle göstermektedir. Bu çerçeve, maymun çiçeği bulaşmasının ve kontrolünün anlaşılmasına katkı sağlamaktadır. Gelecekteki çalışmalar, asemptomatik, presimptomatik ve tedavi altındaki bireyleri ekleyerek modelin geliştirilmesini hedeflemektedir.

Anahtar Kelimeler

• Maymun çiçeği modellemesi
• Aşılamanın etkisi
• Karantina stratejisi
• Hastaneye yatış etkisi
• Kararlılık analizi

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