Mathematical Modeling Of Seir Model With Generalized Incidence Function And The Extension To Covid-19 Model

الموضوعات

علوم بحتة وطبيعية

الملخص

The COVID-19 pandemic had shown the importance of the SEIR model in predicting the outcome of the disease spread and to find the best strategies to contain the pandemic. As this type of model has a limited number of compartments, many other models were derived from the SEIR model to cover, to the maximum, the complex dynamics of the disease spread. These extensions of the SEIR model bring natural validity questions: How can we validate these models? and how far/close are these extended models from giving us real insights into the pandemic? This thesis investigates the SEIR epidemic model and the extended SEAIHR model with generalized incidence functions. We study first the positivity and uniqueness of solutions of both models. Next, we find the disease-free equilibrium points, the endemic equilibrium points, and the basic reproduction number given in both models. Jacobian and basic reproduction numbers are used to obtain the local stability of the equilibrium points. By constructing Lyapunov functions, we find the conditions of the global stability of the disease-free equilibrium, and establishing another Lyapunov function depends on the basic reproduction number to acquire the stability of the endemic equilibrium. Our investigation shows that the disease-free equilibrium is locally asymptotically stable if ℛ 0 0 > 1 there exists at least one endemic equilibrium which can be locally stable. To confirm the theoretical results and study the impact of parameters on the variables in the model we performed numerical simulations via local sensitivity of the parameters with respect to the variables and elasticity with respect to the basic reproduction number in both models. As well as, investigated the impact of different incidence functions of SEIR and SEAIHR models. Our findings confirm that extending the SEIR model can not be affected by the type of incidence. However, increasing the number of parameters creates more sensitivity issues in the model, which requires a careful estimation of COVID-19 in order to get an adequate prediction of the extended model.

روابط وملفات

التعريف والنوع

رقم الوثيقة

faaac604-3a01-4780-ad93-1bb86e64a916

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل ماجيستير

نوع الملف

pdf text

أسماء الملفات

2325345_2.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":"Abdessamad Tridane","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"Shymaa Mohammad Dadoa ","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

English

المصدر والدورية

اسم المصدر

Mathematical Modeling Of Seir Model With Generalized Incidence Function And The Extension To Covid-19 Model

المحتوى والصفحات

عدد الصفحات

0

إشراف وإعداد

الإشراف

Abdessamad Tridane

الإعداد

Shymaa Mohammad Dadoa

الاقتباسات الببليوغرافية