Modeling and analysis of the transmission dynamics of mosquito-borne disease with environmental temperature fluctuation

Modeling And Analysis ◽

Vector Borne Diseases ◽

Proposed Model ◽

Functional Forms ◽

Vector Borne

Most of the vector-borne diseases show a clear dependence on seasonal variation, including climate change. In this paper, we proposed a nonautonomous mathematical model consisting of a periodic system of nonlinear differential equations. In the proposed model, the realistic functional forms for the different temperature-dependent parameters are considered. The autonomous system of the proposed model is also analyzed. The nontrivial solution of the autonomous model is locally asymptotically stable if [Formula: see text]. It is shown that a unique endemic equilibrium point of the autonomous model exists when [Formula: see text] and proved that endemic solution is linearly stable when [Formula: see text]. The nonautonomous model is shown to have a nontrivial disease-free periodic state, which is globally asymptotically stable whenever temperature-dependent reproduction number is less than unity. It is observed that a unique positive endemic periodic solution of the nonautonomous system exists only when a temperature-dependent reproduction number greater than unity, which makes for the persistence of the disease. Numerical simulation has been carried out to support the analytical results and shows the effects of temperature variability in the life span of mosquitoes as well as the persistence of the disease.

On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination

International Journal of Differential Equations ◽

10.1155/2018/4168061 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Author(s):

Stanislas Ouaro ◽

Ali Traoré

Keyword(s):

Basic Reproduction Number ◽

Reproduction Number ◽

Mass Action ◽

Global Dynamics ◽

Asymptotically Stable ◽

Vector Borne Disease ◽

Special Cases ◽

Vector Borne ◽

We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable; that is, the disease dies out, while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable, which means that the disease persists in the population. Using the basic reproduction number, we derive a vaccination coverage rate that is required for disease control and elimination.

A Mathematical Model of COVID-19 Pandemic: A Case Study of Bangkok, Thailand

Computational and Mathematical Methods in Medicine ◽

10.1155/2021/6664483 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Pakwan Riyapan ◽

Sherif Eneye Shuaib ◽

Arthit Intarasit

Keyword(s):

Mathematical Model ◽

Reproduction Number ◽

Transmission Dynamics ◽

Asymptotically Stable ◽

Proposed Model ◽

Next Generation Matrix ◽

Disease Free ◽

In this study, we propose a new mathematical model and analyze it to understand the transmission dynamics of the COVID-19 pandemic in Bangkok, Thailand. It is divided into seven compartmental classes, namely, susceptible S , exposed E , symptomatically infected I s , asymptomatically infected I a , quarantined Q , recovered R , and death D , respectively. The next-generation matrix approach was used to compute the basic reproduction number denoted as R cvd 19 of the proposed model. The results show that the disease-free equilibrium is globally asymptotically stable if R cvd 19 < 1 . On the other hand, the global asymptotic stability of the endemic equilibrium occurs if R cvd 19 > 1 . The mathematical analysis of the model is supported using numerical simulations. Moreover, the model’s analysis and numerical results prove that the consistent use of face masks would go on a long way in reducing the COVID-19 pandemic.

A Fractional Order Dengue Fever Model in the Context of Protected Travellers

10.1101/2021.01.09.21249522 ◽

2021 ◽

Author(s):

E. Bonyah ◽

M. L. Juga ◽

C. W. Chukwu ◽

Fatmawati

Keyword(s):

Dengue Fever ◽

Fractional Order ◽

Existence And Uniqueness ◽

Climate Changes ◽

Reproduction Number ◽

Asymptotically Stable ◽

Qualitative Information ◽

Uniqueness Of Solutions ◽

Vector Borne Diseases ◽

Vector Borne

AbstractClimate changes are affecting the control of many vector-borne diseases, particularly in Africa. In this work, a dengue fever model with protected travellers is formulated. Caputo-Fabrizio operator is utilized to obtain some qualitative information about the disease. The basic properties and the reproduction number is studied. The two steady states are determined and the local stability of the states are found to be asymptotically stable. The fixed pointed theory is made use to obtain the existence and uniqueness of solutions of the model. The numerical simulation suggests that the fractional-order affects the dynamics of dengue fever.

Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2020/4903168 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12 ◽

Author(s):

Bouchaib Khajji ◽

Abderrahim Labzai ◽

Omar Balatif ◽

Mostafa Rachik

Keyword(s):

Alcohol Drinking ◽

Addiction Treatment ◽

Reproduction Number ◽

Dynamical Behavior ◽

Model Parameters ◽

Asymptotically Stable ◽

Modeling And Analysis ◽

Private And Public ◽

The Stability

In this paper, we present a continuous mathematical model PMHTrTpQ of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number R0. We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number R0. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium E0 when R0≤1. When R0>1, drinking present equilibrium E∗ exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium E∗.

Dynamics of a vector-borne model with direct transmission and age of infection.

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2021019 ◽

2021 ◽

Author(s):

Necibe Tuncer ◽

Sunil Giri

Keyword(s):

Basic Reproduction Number ◽

Reproduction Number ◽

Endemic Equilibrium ◽

Asymptotically Stable ◽

Direct Transmission ◽

Born Model ◽

Age Of Infection ◽

Vector Borne ◽

In this paper we the study of dynamics of time since infection structured vector born model with the direct transmission. We use standard incidence term to model the new infections. We analyze the corresponding system of partial di erential equation and obtain an explicit formula for the basic reproduction number R0. The diseases-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one, R0 < 1. Endemic equilibrium exists and is locally asymptotically stable when R0 > 1. The disease will persist at the endemic equilibrium whenever the basic reproduction number is greater than one.

Dynamics of COVID-19 Epidemic Model with Asymptomatic Infection, Quarantine, Protection and Vaccination

Communication in Biomathematical Sciences ◽

10.5614/cbms.2021.4.2.3 ◽

2021 ◽

Vol 4 (2) ◽

pp. 106-124

Author(s):

Raqqasyi Rahmatullah Musafir ◽

Agus Suryanto ◽

Isnani Darti

Keyword(s):

Equilibrium Point ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Asymptomatic Infection ◽

Asymptotically Stable ◽

Proposed Model ◽

Disease Free ◽

We discuss the dynamics of new COVID-19 epidemic model by considering asymptomatic infections and the policies such as quarantine, protection (adherence to health protocols), and vaccination. The proposed model contains nine subpopulations: susceptible (S), exposed (E), symptomatic infected (I), asymptomatic infected (A), recovered (R), death (D), protected (P), quarantined (Q), and vaccinated (V ). We first show the non-negativity and boundedness of solutions. The equilibrium points, basic reproduction number, and stability of equilibrium points, both locally and globally, are also investigated analytically. The proposed model has disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable if basic reproduction number is less than one. The endemic equilibrium point exists uniquely and is globally asymptotically stable if the basic reproduction number is greater than one. These properties have been confirmed by numerical simulations using the fourth order Runge-Kutta method. Numerical simulations show that the disease transmission rate of asymptomatic infection, quarantine rates, protection rate, and vaccination rates affect the basic reproduction number and hence also influence the stability of equilibrium points.

Mathematical Modelling of Human African Trypanosomiasis Using Control Measures

Computational and Mathematical Methods in Medicine ◽

10.1155/2018/5293568 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13 ◽

Cited By ~ 4

Author(s):

Hamenyimana Emanuel Gervas ◽

Nicholas Kwasi-Do Ohene Opoku ◽

Shamsuddeen Ibrahim

Keyword(s):

Human African Trypanosomiasis ◽

Reproduction Number ◽

Tsetse Fly ◽

Control Measures ◽

Asymptotically Stable ◽

African Trypanosomiasis ◽

Vector Borne ◽

Next Generation Matrix ◽

Disease Free

Human African trypanosomiasis (HAT), commonly known as sleeping sickness, is a neglected tropical vector-borne disease caused by trypanosome protozoa. It is transmitted by bites of infected tsetse fly. In this paper, we first present the vector-host model which describes the general transmission dynamics of HAT. In the tsetse fly population, the HAT is modelled by three compartments, while in the human population, the HAT is modelled by four compartments. The next-generation matrix approach is used to derive the basic reproduction number, R0, and it is also proved that if R0≤1, the disease-free equilibrium is globally asymptotically stable, which means the disease dies out. The disease persists in the population if the value of R0>1. Furthermore, the optimal control model is determined by using the Pontryagin’s maximum principle, with control measures such as education, treatment, and insecticides used to optimize the objective function. The model simulations confirm that the use of the three control measures is very efficient and effective to eliminate HAT in Africa.

Dynamic analysis based on the relapse rate of drug epidemic model

International Journal of Biomathematics ◽

10.1142/s1793524521500522 ◽

2021 ◽

pp. 2150052

Author(s):

Lu Niu ◽

Xiaoyun Wang

Keyword(s):

Epidemic Model ◽

Human Population ◽

Drug Users ◽

Reproduction Number ◽

Control Strategies ◽

Asymptotically Stable ◽

Proposed Model ◽

Number Formula ◽

Drug Free

In this paper, we study a drug epidemic model based on epidemiology by dividing the human population into four classes at time [Formula: see text]: susceptibles (S), drug users (I), drug users who are treated in isolation and temporarily quit drugs[Formula: see text] and drug users who are treated in isolation and permanently quit drugs [Formula: see text]. We obtain the basic reproduction number [Formula: see text] of the model and perform its sensitivity analysis. We show that if [Formula: see text], then the drug-free equilibrium is globally asymptotically stable, and if [Formula: see text], there exists an drug-abuse equilibrium and it is locally asymptotically stable. The proposed model may possess forward and backward bifurcations. Moreover, three different control strategies and numerical results are presented. Through different adjustments to obtain graphical results, we obtain the best strategy to control the drug epidemic.

The backward bifurcation of a model for malaria infection

International Journal of Biomathematics ◽

10.1142/s1793524518500183 ◽

2018 ◽

Vol 11 (02) ◽

pp. 1850018 ◽

Author(s):

Juan Wang ◽

Xue-Zhi Li ◽

Souvik Bhattacharya

Keyword(s):

Malaria Infection ◽

Reproduction Number ◽

Backward Bifurcation ◽

Endemic Equilibrium ◽

Asymptotically Stable ◽

Global Asymptotical Stability ◽

Vector Borne ◽

Disease Free ◽

In this paper, an epidemic model of a vector-borne disease, namely, malaria, is considered. The explicit expression of the basic reproduction number is obtained, the local and global asymptotical stability of the disease-free equilibrium is proved under certain conditions. It is shown that the model exhibits the phenomenon of backward bifurcation where the stable disease-free equilibrium coexists with a stable endemic equilibrium. Further, it is proved that the unique endemic equilibrium is globally asymptotically stable under certain conditions.

NUMERICAL AND STABILITY ANALYSIS OF THE TRANSMISSION DYNAMICS OF SVIR EPIDEMIC MODEL WITH STANDARD INCIDENCE RATE

MALAYSIAN JOURNAL OF COMPUTING ◽

10.24191/mjoc.v4i2.5828 ◽

2019 ◽

Vol 4 (2) ◽

pp. 349 ◽

Author(s):

Oluwatayo Michael Ogunmiloro ◽

Fatima Ohunene Abedo ◽

Hammed Kareem

Keyword(s):

Reproduction Number ◽

Disease Spread ◽

Asymptotically Stable ◽

Equilibrium Solutions ◽

Transform Method ◽

Differential Transform ◽

Mathematical Techniques ◽

Fourth Order Method ◽

Theoretical Results

In this article, a Susceptible – Vaccinated – Infected – Recovered (SVIR) model is formulated and analysed using comprehensive mathematical techniques. The vaccination class is primarily considered as means of controlling the disease spread. The basic reproduction number (Ro) of the model is obtained, where it was shown that if Ro<1, at the model equilibrium solutions when infection is present and absent, the infection- free equilibrium is both locally and globally asymptotically stable. Also, if Ro>1, the endemic equilibrium solution is locally asymptotically stable. Furthermore, the analytical solution of the model was carried out using the Differential Transform Method (DTM) and Runge - Kutta fourth-order method. Numerical simulations were carried out to validate the theoretical results.