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Mathematical Models of Infectious Diseases

Humanity has the ability to control the environment within which it resides. In day-to-day life, humans interact with different beings cohabiting their world. These interactions can sometimes be harmful or destructive to living beings and humans, and as a result, humanity has developed techniques, weapons and sophisticated technological instruments to help reduce the threat. Despite technological advances, we are continuously exposed to new challenges, and constantly face biological threats within our environment. Viruses are one such threat. Invisible to the human eye, they live in the air, soil, and water and on material surfaces and are responsible for a number of diseases that kill millions of people. Most recently, the rise of a new strain of coronavirus SARS-COV-2 developed into a pandemic that claimed over 200,000 lives between its first documented case in December 2019 in Wuhan, China, and May 1, 2020.

To combat these invisible enemies, we rely on the study of their behaviors in laboratories, analysis, and prediction. To perform the analysis and prediction, observed facts are converted into models using mathematical tools, including, differentiation, integration and statistical approaches. These models are analyzed and solved analytically or numerically for prediction using some obtained parameters and initial conditions. This present special issue is devoted to a collection of latest results from theoretical to application on research based on infectious diseases.

Edited by: Abdon Atangana, Muhammad Altaf Khan, Jose Francisco Gomez Aguila, Dumitru Baleanu, Emile Franc Doungmo Goufo, Abdullahi Yusuf

  1. Humans are always exposed to the threat of infectious diseases. It has been proven that there is a direct link between the strength or weakness of the immune system and the spread of infectious diseases such a...

    Authors: Behzad Ghanbari

    Citation: Advances in Difference Equations 2020 2020:585

    Content type: Research

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  2. We consider a four-dimensional HIV model that includes healthy cells, infected cells, primary cytotoxic T-lymphocyte response (CTLp), and secondary cytotoxic T-lymphocyte response (CTLe). The CTL memory genera...

    Authors: Chunhua Liu and Lei Kong

    Citation: Advances in Difference Equations 2020 2020:581

    Content type: Research

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  3. The purpose of this article is to discuss the dynamics of the spread of Ebola virus disease (EVD), a kind of fever commonly known as Ebola hemorrhagic fever. It is rare but severe and is considered to be extre...

    Authors: Muhammad Rafiq, Waheed Ahmad, Mujahid Abbas and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:540

    Content type: Research

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  4. Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. This paper provides a numerical solution for the mathematical model of the novel coronavirus by the application...

    Authors: Elham Hashemizadeh and Mohammad Ali Ebadi

    Citation: Advances in Difference Equations 2020 2020:527

    Content type: Research

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  5. Alcoholism is a social phenomenon that affects all social classes and is a chronic disorder that causes the person to drink uncontrollably, which can bring a series of social problems. With this motivation, a ...

    Authors: Zizhen Zhang, Junchen Zou and Soumen Kundu

    Citation: Advances in Difference Equations 2020 2020:522

    Content type: Research

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  6. The aim of the present study is to consider a heroin epidemic model with age-structure only in the active heroin users. The model was formulated with the help of available literature on heroin epidemic. Instea...

    Authors: Anwarud Din and Yongjin Li

    Citation: Advances in Difference Equations 2020 2020:521

    Content type: Research

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  7. Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIR...

    Authors: F. A. Rihan, H. J. Alsakaji and C. Rajivganthi

    Citation: Advances in Difference Equations 2020 2020:502

    Content type: Research

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  8. A simple deterministic epidemic model for tuberculosis is addressed in this article. The impact of effective contact rate, treatment rate, and incomplete treatment versus efficient treatment is investigated. W...

    Authors: Ihsan Ullah, Saeed Ahmad, Qasem Al-Mdallal, Zareen A. Khan, Hasib Khan and Aziz Khan

    Citation: Advances in Difference Equations 2020 2020:499

    Content type: Research

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  9. To forecast the spread tendency of the COVID-19 in China and provide effective strategies to prevent the disease, an improved SEIR model was established. The parameters of our model were estimated based on col...

    Authors: Deshun Sun, Li Duan, Jianyi Xiong and Daping Wang

    Citation: Advances in Difference Equations 2020 2020:489

    Content type: Research

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  10. This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivat...

    Authors: Samia Bushnaq, Kamal Shah and Hussam Alrabaiah

    Citation: Advances in Difference Equations 2020 2020:487

    Content type: Research

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  11. In this paper, a novel coronavirus infection system with a fuzzy fractional differential equation defined in Caputo’s sense is developed. By using the fuzzy Laplace method coupled with Adomian decomposition tr...

    Authors: S. Ahmad, A. Ullah, K. Shah, S. Salahshour, A. Ahmadian and T. Ciano

    Citation: Advances in Difference Equations 2020 2020:472

    Content type: Research

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  12. Acknowledging many effects on humans, which are ignored in deterministic models for COVID-19, in this paper, we consider stochastic mathematical model for COVID-19. Firstly, the formulation of a stochastic sus...

    Authors: Zizhen Zhang, Anwar Zeb, Sultan Hussain and Ebraheem Alzahrani

    Citation: Advances in Difference Equations 2020 2020:451

    Content type: Research

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  13. In the present paper, we formulate a new mathematical model for the dynamics of COVID-19 with quarantine and isolation. Initially, we provide a brief discussion on the model formulation and provide relevant ma...

    Authors: Muhammad Altaf Khan, Abdon Atangana, Ebraheem Alzahrani and Fatmawati

    Citation: Advances in Difference Equations 2020 2020:425

    Content type: Research

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  14. In this work, we study the dengue dynamics with fractal-factional Caputo–Fabrizio operator. We employ real statistical data of dengue infection cases of East Java, Indonesia, from 2018 and parameterize the den...

    Authors: Fatmawati, Muhammad Altaf Khan, Cicik Alfiniyah and Ebraheem Alzahrani

    Citation: Advances in Difference Equations 2020 2020:422

    Content type: Research

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  15. One of the control measures available that are believed to be the most reliable methods of curbing the spread of coronavirus at the moment if they were to be successfully applied is lockdown. In this paper a m...

    Authors: Idris Ahmed, Isa Abdullahi Baba, Abdullahi Yusuf, Poom Kumam and Wiyada Kumam

    Citation: Advances in Difference Equations 2020 2020:394

    Content type: Research

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  16. The aim of this work is to present a new fractional order model of novel coronavirus (nCoV-2019) under Caputo–Fabrizio derivative. We make use of fixed point theory and Picard–Lindelöf technique to explore the...

    Authors: Azhar Hussain, Dumitru Baleanu and Muhammad Adeel

    Citation: Advances in Difference Equations 2020 2020:384

    Content type: Research

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  17. Since the first case of 2019 novel coronavirus disease (COVID-19) detected on 30 January, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April, 2020. Taking th...

    Authors: Amjad Salim Shaikh, Iqbal Najiroddin Shaikh and Kottakkaran Sooppy Nisar

    Citation: Advances in Difference Equations 2020 2020:373

    Content type: Research

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  18. Lately, many studies were offered to introduce the population dynamics of COVID-19. In this investigation, we extend different physical conditions of the growth by employing fractional calculus. We study a sys...

    Authors: Samir B. Hadid, Rabha W. Ibrahim, Dania Altulea and Shaher Momani

    Citation: Advances in Difference Equations 2020 2020:338

    Content type: Research

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  19. In this manuscript, the fractional Atangana–Baleanu–Caputo model of prey and predator is studied theoretically and numerically. The existence and Ulam–Hyers stability results are obtained by applying fixed poi...

    Authors: Mohammed S. Abdo, Satish K. Panchal, Kamal Shah and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2020 2020:249

    Content type: Research

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