Mathematical modeling of the impact of temperature variations and immigration on malaria prevalence in Nigeria

2021 ◽  
pp. 2150067
Author(s):  
Eunice E. Ukwajunor ◽  
Eno E. E. Akarawak ◽  
Israel Olutunji Abiala
Keyword(s):  
Equilibrium Point ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Malaria Incidence ◽  
Malaria Prevalence ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Marginal Effect ◽  
Asymptotically Stable ◽  
The Impact

The study examines the population-level impact of temperature variability and immigration on malaria prevalence in Nigeria, using a novel deterministic model. The model incorporates disease transmission by immigrants into the community. In the absence of immigration, the model is shown to exhibit the phenomenon of backward bifurcation. The disease-free equilibrium of the autonomous version of the model was found to be locally asymptotically stable in the absence of infective immigrants. However, the model exhibits an endemic equilibrium point when the immigration parameter is greater than zero. The endemic equilibrium point is seen to be globally asymptotically stable in the absence of disease-induced mortality. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to malaria transmission dynamics in Nigeria, shows that the top three parameters that drive malaria prevalence (with respect to [Formula: see text]) are the mosquito natural death rate ([Formula: see text]), mosquito biting rate ([Formula: see text]) and the transmission rates between humans and mosquitoes ([Formula: see text]). Numerical simulations of the model show that in Nigeria, malaria burden increases with increasing mean monthly temperature in the range of 22–28[Formula: see text]. Thus, this study suggests that control strategies for malaria should be intensified during this period. It is further shown that the proportion of infective immigrants has marginal effect on the transmission dynamics of the disease. Therefore, the simulations suggest that a reduction in the fraction of infective immigrants, either exposed or infectious, would significantly reduce the malaria incidence in a population.

scholarly journals A Mathematical Model of a Tuberculosis Transmission Dynamics Incorporating First and Second Line Treatment

2020 ◽  
Vol 24 (5) ◽  
pp. 917-922
Author(s):  
J. Andrawus ◽  
F.Y. Eguda ◽  
I.G. Usman ◽  
S.I. Maiwa ◽  
I.M. Dibal ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Line Treatment ◽  
Second Line ◽  
Tuberculosis Transmission ◽  
Disease Free

This paper presents a new mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment. We calculated a control reproduction number which plays a vital role in biomathematics. The model consists of two equilibrium points namely disease free equilibrium and endemic equilibrium point, it has been shown that the disease free equilibrium point was locally asymptotically stable if thecontrol reproduction number is less than one and also the endemic equilibrium point was locally asymptotically stable if the control reproduction number is greater than one. Numerical simulation was carried out which supported the analytical results. Keywords: Mathematical Model, Biomathematics, Reproduction Number, Disease Free Equilibrium, Endemic Equilibrium Point

Analysis of a mathematical model for the transmission dynamics of human melioidosis

2020 ◽  
Vol 13 (07) ◽  
pp. 2050062
Author(s):  
Yibeltal Adane Terefe ◽  
Semu Mitiku Kassa
Keyword(s):  
Human Population ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Disease Dynamics ◽  
Number Formula ◽  
Disease Free

A deterministic model for the transmission dynamics of melioidosis disease in human population is designed and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the basic reproduction number [Formula: see text] is less than one. It is further shown that the backward bifurcation dynamics is caused by the reinfection of individuals who recovered from the disease and relapse. The existence of backward bifurcation implies that bringing down [Formula: see text] to less than unity is not enough for disease eradication. In the absence of backward bifurcation, the global asymptotic stability of the disease-free equilibrium is shown whenever [Formula: see text]. For [Formula: see text], the existence of at least one locally asymptotically stable endemic equilibrium is shown. Sensitivity analysis of the model, using the parameters relevant to the transmission dynamics of the melioidosis disease, is discussed. Numerical experiments are presented to support the theoretical analysis of the model. In the numerical experimentations, it has been observed that screening and treating individuals in the exposed class has a significant impact on the disease dynamics.

scholarly journals Transmission Dynamics of Hepatitis C with Control Strategies

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Adnan Khan ◽  
Sultan Sial ◽  
Mudassar Imran
Keyword(s):  
Optimal Control ◽  
Hepatitis C ◽  
Deterministic Model ◽  
Control Strategies ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Critical Parameters ◽  
Optimal Controls ◽  
Infected Population ◽  
The Impact

We present a rigorous mathematical analysis of a deterministic model, for the transmission dynamics of hepatitis C, using a standard incidence function. The infected population is divided into three distinct compartments featuring two distinct infection stages (acute and chronic) along with an isolation compartment. It is shown that for basic reproduction number R0≤1, the disease-free equilibrium is locally and globally asymptotically stable. The model also has an endemic equilibrium for R0>1. Uncertainty and sensitivity analyses are carried out to identify and study the impact of critical parameters on R0. In addition, we have presented the numerical simulations to investigate the influence of different important parameters on R0. Since we have a locally stable endemic equilibrium, optimal control is applied to the deterministic model to reduce the total infected population. Two different optimal control strategies (vaccination and isolation) are designed to control the disease and reduce the infected population. Pontryagin’s Maximum Principle is used to characterize the optimal controls in terms of an optimality system which is solved numerically. Numerical results for the optimal controls are compared against the constant controls and their effectiveness is discussed.

scholarly journals Modeling Tuberculosis Among Healthcare Workers

2019 ◽  
Vol 5 (2) ◽  
pp. 186-196
Author(s):  
T.S. Faniran ◽  
A.O. Falade ◽  
T.O. Alakija
Keyword(s):  
Sensitivity Analysis ◽  
Equilibrium Point ◽  
Healthcare Workers ◽  
Compliance Rate ◽  
Transmission Dynamics ◽  
Infectious Period ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Susceptible Population ◽  
The Impact

AbstractA mathematical model for transmission dynamics of tuberculosis among healthcare workers is formulated. Tuberculosis is an airborne disease caused by Mycobacterium tuberculosis bacteria that affect the lungs of a host. Previous research had concentrated on mathematical modeling of transmission dynamics of tuberculosis without considering the impact of compliance rate to particulate respirator by healthcare workers on the transmission. Therefore, how compliance rate to particulate respirator reduces the transmission of tuberculosis is an active question, and we develop a new system of ordinary differential equations that explicitly explores the impact of compliance rate to particulate respirator by healthcare workers upon transmission. Rigorous analysis of the model shows that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number, Ro < 1. This is established through the analysis of characteristic equation. Basic reproduction, Ro is the number of new cases that an existing case generates on average over the infectious period in a susceptible population. We also show that the endemic equilibrium point is locally asymptotically stable for Ro > 1, by using Routh-Hurwitz criteria for stability. Sensitivity analysis is carried out to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is β (Human-to-human transmission rate), followed by Λ (Human recruitment rate). Also, the result shows that increase in ψ (compliance rate to particulate respirator by healthcare workers) leads to decrease in Ro which reduces tuberculosis spread among healthcare workers.

scholarly journals Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Ebrima Kanyi ◽  
Ayodeji Sunday Afolabi ◽  
Nelson Owuor Onyango
Keyword(s):  
Equilibrium Point ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Modeling And Analysis ◽  
Disease Free

This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R 0 , is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R 0 > 1 . It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R 0 < 1 , and the unique endemic equilibrium point is locally asymptotically stable whenever R 0 > 1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R 0 = 1 , the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R 0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis.

scholarly journals Modeling the Effect of Inpatient Rehabilitation of Tobacco Smokers on Smoking Dynamics

2021 ◽  
pp. 1-14
Author(s):  
Amos Mwendwa Nyamai ◽  
Winifred N. Mutuku
Keyword(s):  
Stability Analysis ◽  
Equilibrium Point ◽  
Tobacco Smoking ◽  
Smoking Habit ◽  
Inpatient Rehabilitation ◽  
The Body ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Impact

Aims: Develop and analyze a mathematical model of the effect of inpatient rehabilitation of tobacco smokers on tobacco smoking using Kenya as a case study. Perform stability analysis on the smoking free equilibrium point and endemic equilibrium point of the model. Use numerical simulation to investigate the impact of inpatient rehabilitation of tobacco smokers on smoking. Place and Duration of Study: Department of Mathematics and Actuarial Science, School of Pure and Applied Sciences (SPAS), Kenyatta University, Kenya, between May 2019 and September 2020. Tobacco smoking is a serious burden in Kenya and the world at large. Smoking harms nearly every organ of the body and affects the overall health of a person. Despite the overwhelming facts about the consequences of tobacco smoking, it remains a bad wont which is socially accepted and widely spread. In this research we numerically analyze the dynamics of smoking incorporating the impact of inpatient rehabilitation to curb the smoking habit. We first present a three-compartment model incorporating inpatient rehabilitation, then develop the system of ordinary differential equations governing the smoking dynamics. The basic reproduction number is determined using next generation matrix method. The model equilibria were computed and the stability analysis carried out. The results of stability analysis indicate that the disease-free equilibrium (DFE) is both locally and globally asymptotically stable for RS < 1 while the endemic equilibrium is both locally and globally asymptotically stable for RS > 1. Numerical simulations of model carried out with the help of MATLAB shows that, when rehabilitation is implemented effectively, it helps in minimization of smoking in the community.

scholarly journals Modeling the Impact of Vaccination, Screening, Treatment on the Dynamics of Pneumonia

2020 ◽  
Vol 12 (4) ◽  
pp. 525-536
Author(s):  
K. S. Rahman ◽  
S. R. Mitkari ◽  
S. Shaikh
Keyword(s):  
Equilibrium Point ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Infected Individual ◽  
Nonlinear Ordinary Differential Equation ◽  
Endemic Equilibrium ◽  
Natural Immunity ◽  
The Stability ◽  
The Impact

In this paper we have presented a deterministic model for pneumonia transmission and we have used the model to avail the potential impact of therapy. The model is based on the vaccinated-susceptible-carrier-infected-recovered-susceptible compartmental structure and their possible interventions with the possibility of infected individual recovery from natural immunity. Here, we have modeled Pneumonia considering vaccination, screening and treatment with a system of nonlinear ordinary differential equation. The model reproduction number R0 is derived and the stability of the equilibria are derived. The stability of equilibrium points is analyzed. The results shows that there exists a locally stable disease free equilibrium points, E0 when R0<1 and a unique endemic equilibrium E1, when R0>1. Infection free point was found to be locally stable and if reproduction number is greater than unity, then there is unique endemic equilibrium point and if it is less than unity, the endemic equilibrium point is globally asymptotically stable and pneumonia will be eliminated.

scholarly journals Stability analysis of a dynamical model of tuberculosis with incomplete treatment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ihsan Ullah ◽  
Saeed Ahmad ◽  
Qasem Al-Mdallal ◽  
Zareen A. Khan ◽  
Hasib Khan ◽  
...  
Keyword(s):  
Disease Transmission ◽  
Contact Rate ◽  
Asymptotically Stable ◽  
Treatment Rate ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Efficient Treatment ◽  
Effective Contact ◽  
The Impact ◽  
Incomplete Treatment

Abstract 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. We also analyze the asymptotic behavior, spread, and possible eradication of the TB infection. It is observed that the disease transmission dynamics is characterized by the basic reproduction ratio $\Re _{0}$ ℜ 0 ; if $\Re _{0}<1$ ℜ 0 < 1 , there is only a disease-free equilibrium which is both locally and globally asymptotically stable. Moreover, for $\Re _{0}>1$ ℜ 0 > 1 , a unique positive endemic equilibrium exists which is globally asymptotically stable. The global stability of the equilibria is shown via Lyapunov function. It is also obtained that incomplete treatment of TB causes increase in disease infection while efficient treatment results in a reduction in TB. Finally, for the estimated parameters, some numerical simulations are performed to verify the analytical results. These numerical results indicate that decrease in the effective contact rate λ and increase in the treatment rate γ play a significant role in the TB infection control.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

Sign in / Sign up

Export Citation Format

Share Document