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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. Epidemiological models have been playing a vital role in different areas of biological sciences for the analysis of various contagious diseases. Transmissibility of virulent diseases is being portrayed in the ...

    Authors: Abdullah Khamis Alzahrani, Oyoon Abdul Razzaq, Najeeb Alam Khan, Ali Saleh Alshomrani and Malik Zaka Ullah

    Citation: Advances in Difference Equations 2021 2021:292

    Content type: Research

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  2. In this study, we develop a nonlinear ordinary differential equation to study the dynamics of syphilis transmission incorporating controls, namely prevention and treatment of the infected males and females. We...

    Authors: Abdulfatai Atte Momoh, Yusuf Bala, Dekera Jacob Washachi and Dione Déthié

    Citation: Advances in Difference Equations 2021 2021:285

    Content type: Research

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  3. This work investigates the dissemination mechanism of pine wilt disease. The basic reproduction number is computed explicitly, and an ultimate invariable level of contagious hosts and vectors, without and with...

    Authors: Riaz Ahmad Khan, Takasar Hussain, Muhammad Ozair, Fatima Tasneem and Muhammad Faizan

    Citation: Advances in Difference Equations 2021 2021:261

    Content type: Research

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  4. In this manuscript, we investigate a novel Susceptible–Exposed–Infected–Quarantined–Recovered (SEIQR) COVID-19 propagation model with two delays, and we also consider supply chain transmission and hierarchical...

    Authors: Fangfang Yang and Zizhen Zhang

    Citation: Advances in Difference Equations 2021 2021:191

    Content type: Research

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  5. This manuscript is involved in the study of stability of the solutions of functional differential equations (FDEs) with random coefficients and/or stochastic terms. We focus on the study of different types of ...

    Authors: Abdulwahab Almutairi, H. El-Metwally, M. A. Sohaly and I. M. Elbaz

    Citation: Advances in Difference Equations 2021 2021:186

    Content type: Research

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  6. Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with...

    Authors: Ali S. Alshomrani, Malik Z. Ullah and Dumitru Baleanu

    Citation: Advances in Difference Equations 2021 2021:185

    Content type: Research

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  7. This manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentione...

    Authors: Sabri T. M. Thabet, Mohammed S. Abdo and Kamal Shah

    Citation: Advances in Difference Equations 2021 2021:184

    Content type: Research

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  8. The article is based on the study of hepatitis transmission dynamics using a stochastic epidemic model. We discuss the stochastic perturbations of our proposed model by considering the effect of environmental ...

    Authors: Amir Khan, Ghulam Hussain, Abdullahi Yusuf, Auwalu Hamisu Usman and Usa Wannasingha Humphries

    Citation: Advances in Difference Equations 2021 2021:181

    Content type: Research

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  9. In the present paper, based on the conditions that asymptomatic virus carriers are contagious and all symptomatic infected individuals wear masks, we study the impact of wearing masks in the susceptible and th...

    Authors: Lili Han, Qiuhui Pan, Baolin Kang and Mingfeng He

    Citation: Advances in Difference Equations 2021 2021:169

    Content type: Research

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  10. In this study we propose a fractional frequency flexible Fourier form fractionally integrated ADF unit-root test, which combines the fractional integration and nonlinear trend as a form of the Fourier function...

    Authors: Tolga Omay and Dumitru Baleanu

    Citation: Advances in Difference Equations 2021 2021:167

    Content type: Research

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  11. To investigate the influences of heterogeneity and waning immunity on measles transmission, we formulate a network model with periodic transmission rate, and theoretically examine the threshold dynamics. We nu...

    Authors: Yuyi Xue, Xiaoe Ruan and Yanni Xiao

    Citation: Advances in Difference Equations 2021 2021:138

    Content type: Research

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  12. Hand, foot, and mouth disease (HFMD) is a contagious viral illness that commonly affects infants and children. In some areas with high incidence of this disease, the relevant departments often use some strateg...

    Authors: Lei Shi, Hongyong Zhao and Daiyong Wu

    Citation: Advances in Difference Equations 2021 2021:130

    Content type: Research

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  13. In this paper, we have mathematically analyzed a within-host model of SARS-CoV-2 which is used by Li et al. in the paper “The within-host viral kinetics of SARS-CoV-2” published in (Math. Biosci. Eng. 17(4):2853–...

    Authors: Bhagya Jyoti Nath, Kaushik Dehingia, Vishnu Narayan Mishra, Yu-Ming Chu and Hemanta Kumar Sarmah

    Citation: Advances in Difference Equations 2021 2021:113

    Content type: Research

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  14. COVID-19 or coronavirus is a newly emerged infectious disease that started in Wuhan, China, in December 2019 and spread worldwide very quickly. Although the recovery rate is greater than the death rate, the CO...

    Authors: Mohammed A. Aba Oud, Aatif Ali, Hussam Alrabaiah, Saif Ullah, Muhammad Altaf Khan and Saeed Islam

    Citation: Advances in Difference Equations 2021 2021:106

    Content type: Research

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  15. The aim of this research is to construct an SIR model for COVID-19 with fuzzy parameters. The SIR model is constructed by considering the factors of vaccination, treatment, obedience in implementing health pro...

    Authors: Muhammad Abdy, Syafruddin Side, Suwardi Annas, Wahyuddin Nur and Wahidah Sanusi

    Citation: Advances in Difference Equations 2021 2021:105

    Content type: Research

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  16. In this paper, we discuss the Anthroponotic Cutaneous Leishmania transmission. In addition, we develop a mathematical model for the Anthroponotic Cutaneous Leishmania transmission and consider its qualitative ...

    Authors: Karim Khan, Rahat Zarin, Amir Khan, Abdullahi Yusuf, Mohammed Al-Shomrani and Arif Ullah

    Citation: Advances in Difference Equations 2021 2021:86

    Content type: Research

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  17. Using the existing collected data from European and African countries, we present a statistical analysis of forecast of the future number of daily deaths and infections up to 10 September 2020. We presented nu...

    Authors: Abdon Atangana and Seda İğret Araz

    Citation: Advances in Difference Equations 2021 2021:57

    Content type: Research

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  18. In this paper, we study the oscillation of a class of third-order Emden–Fowler delay dynamic equations with sublinear neutral terms on time scales. By using Riccati transformation and integral inequality, we e...

    Authors: Zhiyu Zhang and Ruihua Feng

    Citation: Advances in Difference Equations 2021 2021:53

    Content type: Research

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  19. The development of COVID-19 vaccine is highly concerned by all countries in the world. So far, many kinds of COVID-19 vaccines have entered phase III clinical trial. However, it is difficult to deliver COVID-1...

    Authors: Daoming Dai, Xuanyu Wu and Fengshan Si

    Citation: Advances in Difference Equations 2021 2021:39

    Content type: Research

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  20. Recently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is bas...

    Authors: Rabha W. Ibrahim, Dania Altulea and Rafida M. Elobaid

    Citation: Advances in Difference Equations 2021 2021:9

    Content type: Research

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  21. The novel coronavirus (SARS-CoV-2), or COVID-19, has emerged and spread at fast speed globally; the disease has become an unprecedented threat to public health worldwide. It is one of the greatest public healt...

    Authors: Isaac Owusu-Mensah, Lanre Akinyemi, Bismark Oduro and Olaniyi S. Iyiola

    Citation: Advances in Difference Equations 2020 2020:683

    Content type: Research

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  22. A disastrous coronavirus, which infects a normal person through droplets of infected person, has a route that is usually by mouth, eyes, nose or hands. These contact routes make it very dangerous as no one can...

    Authors: Zizhen Zhang, Anwar Zeb, Ebraheem Alzahrani and Sohail Iqbal

    Citation: Advances in Difference Equations 2020 2020:675

    Content type: Research

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  23. In this paper an SIR deterministic mathematical model for co-infection of dengue and leptospirosis is proposed. We use a compartment model by using ordinary differential equations. The positivity of future sol...

    Authors: Haileyesus Tessema Alemneh

    Citation: Advances in Difference Equations 2020 2020:664

    Content type: Research

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  24. In this manuscript, we investigate a nonlinear delayed model to study the dynamics of human-immunodeficiency-virus in the population. For analysis, we find the equilibria of a susceptible–infectious–immune sys...

    Authors: Ali Raza, Ali Ahmadian, Muhammad Rafiq, Soheil Salahshour, Muhammad Naveed, Massimiliano Ferrara and Atif Hassan Soori

    Citation: Advances in Difference Equations 2020 2020:663

    Content type: Research

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  25. According to the World Health Organization reports, tuberculosis (TB) remains one of the top 10 deadly diseases of recent decades in the world. In this paper, we present the modeling, analysis and simulation o...

    Authors: Selain Kasereka Kabunga, Emile F. Doungmo Goufo and Vinh Ho Tuong

    Citation: Advances in Difference Equations 2020 2020:642

    Content type: Research

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  26. 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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  27. 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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  28. 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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  29. 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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  30. 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

    Published on:

  31. 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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  32. 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

    Published on:

  33. 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

    Published on:

  34. 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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  35. 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

    Published on: