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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

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1. ### On modeling of coronavirus-19 disease under Mittag-Leffler power law

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
2. ### Fuzzy fractional-order model of the novel coronavirus

In this paper, a novel coronavirus infection system with a fuzzy fractional differential equation defined in Caputoâ€™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
3. ### Dynamics of COVID-19 mathematical model with stochastic perturbation

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
4. ### The dynamics of COVID-19 with quarantined and isolation

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
5. ### Analysis of dengue model with fractal-fractional Caputoâ€“Fabrizio operator

In this work, we study the dengue dynamics with fractal-factional Caputoâ€“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

The Correction to this article has been published in Advances in Difference Equations 2021 2021:46

6. ### Modelling intracellular delay and therapy interruptions within Ghanaian HIV population

This paper seeks to unveil the niche of delay differential equation in harmonizing low HIV viral haul and thereby articulating the adopted model, to delve into structured treatment interruptions. Therefore, an...

Authors: Kofi F. Owusu, Emile F. Doungmo Goufo and Stella Mugisha
Citation: Advances in Difference Equations 2020 2020:401
7. ### Analysis of Caputo fractional-order model for COVID-19 with lockdown

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
8. ### New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019-nCoV system

According to the report presented by the World Health Organization, a new member of viruses, namely, coronavirus, shortly 2019-nCoV, which arised in Wuhan, China, on January 7, 2020, has been introduced to the...

Authors: Wei Gao, Haci Mehmet Baskonus and Li Shi
Citation: Advances in Difference Equations 2020 2020:391
9. ### Existence of solution and stability for the fractional order novel coronavirus (nCoV-2019) model

The aim of this work is to present a new fractional order model of novel coronavirus (nCoV-2019) under Caputoâ€“Fabrizio derivative. We make use of fixed point theory and Picardâ€“LindelÃ¶f technique to explore the...

Authors: Azhar Hussain, Dumitru Baleanu and Muhammad Adeel
Citation: Advances in Difference Equations 2020 2020:384
10. ### A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control

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
11. ### Solvability and stability of a fractional dynamical system of the growth of COVID-19 with approximate solution by fractional Chebyshev polynomials

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
12. ### Study of transmission dynamics of novel COVID-19 by using mathematical model

In this research work, we present a mathematical model for novel coronavirus-19 infectious disease which consists of three different compartments: susceptible, infected, and recovered under convex incident rat...

Authors: Rahim Ud Din, Kamal Shah, Imtiaz Ahmad and Thabet Abdeljawad
Citation: Advances in Difference Equations 2020 2020:323
13. ### Existence theory and numerical analysis of three species preyâ€“predator model under Mittag-Leffler power law

In this manuscript, the fractional Atanganaâ€“Baleanuâ€“Caputo model of prey and predator is studied theoretically and numerically. The existence and Ulamâ€“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