Modeling Monkeypox: Spread of Outbreak with Social Distancing, Quarantine and Vaccination

Year 2025, Volume: 14 Issue: 1, 361 - 384, 26.03.2025

Mahir Demir

https://doi.org/10.17798/bitlisfen.1589786

Abstract

In this paper, we introduced a novel mathematical model to simulate the spread of the zoonotic viral disease monkeypox, incorporating both human and rodent populations to capture the disease dynamics. Unlike previous models, we included a quarantine compartment for infected humans, a social distancing compartment for susceptible individuals, and vaccination with direct transmission to the recovered compartment, offering a more comprehensive framework for controlling the spread of monkeypox. We then compared the effectiveness of these three control measures in reducing disease transmission. To investigate the dynamics of the model, we first demonstrated that it has a unique, positive, and bounded solution. Next, we calculated the basic reproduction number, R_0 for the proposed model. A sensitivity analysis is then conducted to identify key parameters, followed by an assessment of their effects on R_0. Additionally, we analyzed the local stability of both the disease-free and endemic equilibrium points to identify the conditions under which the disease dies out or remains endemic. We first showed in stability analysis section that these three control parameters play important roles in stability of equlibrium points. After that our findings in sensitivity analysis indicated the critical role of recovery rates and incubation periods in shaping the outbreak trajectory. Besides them, our analysis of R_0 in 3-D plots showed that the human-to-human transmission (β_hh) has about 3 times greater impact than rodent-to-human transmission (β_rh) on R_0. Finally, we presented simulations to show single and combined effects of the control parameters: quarantine, social distancing and vaccination on the transmission of monkeypox virus.

Keywords

Mpox, sensitivity analysis, infectious disease, basic reproduction number, stability analysis.

Ethical Statement

The study is complied with research and publication ethics.

Maymun Çiçeğinin Modellemesi: Sosyal Mesafe, Karantina ve Aşılama ile Salgının Yayılımı

Abstract

Bu çalışmada, zoonotik bir viral hastalık olan maymun çiçeğinin yayılımını simüle etmek için hem insan hem de kemirgen popülasyonlarını içeren yenilikçi bir matematiksel model sunduk. Önceki modellerden farklı olarak, enfekte insanlar için bir karantina bölmesi, hassas bireyler için bir sosyal mesafe bölmesi ve doğrudan iyileşen bölmeye geçişle birlikte aşılama sürecini ekleyerek maymun çiçeği yayılımını kontrol etmeye yönelik daha kapsamlı bir çerçeve sağladık. Ardından, bu üç kontrol önleminin hastalığın bulaşmasını azaltmadaki etkinliğini karşılaştırdık.Modelin dinamiklerini incelemek için öncelikle modelin çözümünün, tek, pozitif ve sınırlı olduğunu gösterdik. Daha sonra önerilen model için temel üreme sayısını (R_0) hesapladık. Anahtar parametreleri belirlemek için bir duyarlılık analizi gerçekleştirdik ve bu parametrelerin R_0 üzerindeki etkilerini değerlendirdik. Ayrıca, hastalığın yok olduğu veya endemik kaldığı koşulları belirlemek için hem hastalıksız denge noktasının hem de endemik denge noktasının kararlılığını analiz ettik. Bulgularımız, maymun çiçeği dinamiklerini etkileyen temel parametrelerin aşılama, sosyal mesafe ve karantina olduğunu ortaya koydu. Duyarlılık analizi, iyileşme oranlarının ve kuluçka sürelerinin salgın eğrisi üzerindeki kritik rolünü vurguladı. Bunun yanında, insan-insan bulaşmasının (β_hh) kemirgen-insan bulaşmasından (
β_rh) daha büyük bir etkiye sahip olduğunu gösterdik. Kontrolleri eş zamalı olarak birlikte uyguladığımızda, özellikle kontrollerin parametre değerleri belirli seviyelere ulaşıldığında enfekte vakaları büyük ölçüde azaltmaktadır.

Keywords

Mpox, duyarlılık analizi, bulaşıcı hastalık, temel üreme sayısı, kararlılık analizi

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