scholarly journals Enhancing reservoir control in the co-dynamics of HIV-VL: from mathematical modeling perspective

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zinabu Teka Melese ◽  
Haileyesus Tessema Alemneh
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Visceral Leishmaniasis ◽  
Recovery Rate ◽  
Dynamical Behavior ◽  
Contact Rate ◽  
Full Model ◽  
Policy Makers ◽  
Infection Disease ◽  
Disease Free

AbstractHIV patients are vulnerable to developing active visceral leishmaniasis (VL). To understand this complication, we studied a mathematical model for HIV and visceral leishmaniasis coinfection. In this approach, we reckoned two distinct equilibria: the disease-free and the endemic equilibria. The local and global stability of the disease-free equilibrium were thoroughly investigated. To further support the qualitative findings, we performed simulations to quantify the changes of the dynamical behavior of the full model for variation of relevant parameters. Increasing the rate of VL recovery ($\phi _{1}$ ϕ 1 ), the recovery rate for VL–HIV Co-infection ($\phi _{2}$ ϕ 2 ), removing reservoirs ($c_{1}$ c 1 ), minimizing the contact rate ($\beta _{h}$ β h ) are important in controlling the transmission of individual and co-infection disease of VL and HIV. In conclusion, possible measures should be implemented to reduce the number of infected individuals. Therefore, we recommend that policy makers and stakeholders incorporate these measures during planing and implementation phases to control the transmission of VL–HIV co-infection.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

scholarly journals Simple MSEIR Model for Measles Transmission

2019 ◽  
pp. 1-11
Author(s):  
Mojeeb Al-Rahman EL-Nor Osman ◽  
Appiagyei Ebenezer ◽  
Isaac Kwasi Adu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Birth Rate ◽  
Reproduction Number ◽  
Progression Rate ◽  
Asymptotically Stable ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an Immunity-Susceptible-Exposed-Infectious-Recovery (MSEIR) mathematical model was used to study the dynamics of measles transmission. We discussed that there exist a disease-free and an endemic equilibria. We also discussed the stability of both disease-free and endemic equilibria.  The basic reproduction number  is obtained. If , then the measles will spread and persist in the population. If , then the disease will die out.  The disease was locally asymptotically stable if  and unstable if  . ALSO, WE PROVED THE GLOBAL STABILITY FOR THE DISEASE-FREE EQUILIBRIUM USING LASSALLE'S INVARIANCE PRINCIPLE OF Lyaponuv function. Furthermore, the endemic equilibrium was locally asymptotically stable if , under certain conditions. Numerical simulations were conducted to confirm our analytic results. Our findings were that, increasing the birth rate of humans, decreasing the progression rate, increasing the recovery rate and reducing the infectious rate can be useful in controlling and combating the measles.

scholarly journals Stabiizing The Steady State Solution of Lasser Fever: Problems and Prospect

2022 ◽  
Vol 05 (01) ◽  
Author(s):  
Innocent C. Eli ◽  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Control Parameter ◽  
Steady State Solution ◽  
Lassa Fever ◽  
Sexual Contact ◽  
Opposite Sex ◽  
The Stability ◽  
And Control ◽  
Disease Free

The study of mathematical modeling of the stability analysis of Lassa fever was examined. A mathematical model for the spread and control of Lassa fever was formulated and analyzed. The model incorporates a control parameter, the use of condom to control human to human transmission through sexual contact with opposite sex. The disease free and endemic equilibrium states were analyzed.

scholarly journals EFFECTS OF TREATMENT, AWARENESS AND CONDOM USE IN A COINFECTION MODEL FOR HIV AND HCV IN MSM

2015 ◽  
Vol 23 (02) ◽  
pp. 165-193 ◽  
Author(s):  
CARLA M. A. PINTO ◽  
ANA CARVALHO
Keyword(s):  
Human Immunodeficiency Virus ◽  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Full Model ◽  
Bifurcation Diagrams ◽  
Immunodeficiency Virus ◽  
Disease Free ◽  
Qualitative Changes

We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodeficiency virus (HIV). We consider treatment for both diseases, screening, unawareness and awareness of HIV infection, and the use of condoms. We study the local stability of the disease-free equilibria for the full model and for the two submodels (HCV only and HIV only submodels). We sketch bifurcation diagrams for different parameters, such as the probabilities that a contact will result in a HIV or an HCV infection. We present numerical simulations of the full model where the HIV, HCV and double endemic equilibria can be observed. We also show numerically the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. We extrapolate the results from the model for actual measures that could be implemented in order to reduce the number of infected individuals.

scholarly journals Stability of a Mathematical Model of Malaria Transmission with Relapse

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hai-Feng Huo ◽  
Guang-Ming Qiu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Next Generation Matrix ◽  
The Government ◽  
Disease Free ◽  
The Basic Reproduction Number

A more realistic mathematical model of malaria is introduced, in which we not only consider the recovered humans return to the susceptible class, but also consider the recovered humans return to the infectious class. The basic reproduction numberR0is calculated by next generation matrix method. It is shown that the disease-free equilibrium is globally asymptotically stable ifR0≤1, and the system is uniformly persistence ifR0>1. Some numerical simulations are also given to explain our analytical results. Our results show that to control and eradicate the malaria, it is very necessary for the government to decrease the relapse rate and increase the recovery rate.

scholarly journals Mathematical Modeling of Listeriosis Incorporating Effects of Awareness Programs

2020 ◽  
Author(s):  
C. W. Chukwu ◽  
F. Nyabadza
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Infectious Diseases ◽  
Local Stability ◽  
Human Population ◽  
Food Contamination ◽  
Awareness Programs ◽  
The Media ◽  
Control And Management ◽  
Disease Free

AbstractAwareness programs by the media play a pivotal role in the control of infectious diseases. In this paper, we formulate, and analyse a mathematical model for listeriosis with incorporating aware individuals interacting with the infected individuals. The model has three equilibria; namely; the disease-free, the bacteria free, and the endemic equilibria. Local stability of the equilibria were established using the food contamination number . Numerical simulations are carried out and the effects of various parameters on the model variables investigated. The results reveal that an increase in the efficacy of awareness programs, rate of implementation of awareness programs, and the rate at which unaware susceptible becomes awareness result in the reduction of listeriosis in the human population. The result have important implications on the control and management of listeriosis.

scholarly journals Mathematical modeling of COVID-19 spread and stabilization in Madhya Pradesh, India: A fundamental approach

2021 ◽  
Author(s):  
Deepak Kumar ◽  
Vikash Kumar ◽  
Vijay Panchore ◽  
Ravi Kumar Mandava ◽  
Somnath Sarangi
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Recovery Rate ◽  
Madhya Pradesh ◽  
The Other ◽  
Virus Spread ◽  
Good Recovery ◽  
Chain Breaking ◽  
Novel Model

Abstract The present study was performed to model a COVID-19 spread and stabilization constraints for the regional people of Madhya Pradesh, India, at the mid-time of the lockdown period. A novel mathematical model was developed to predict the number of days required to break the virus spread chain based on the chain breaking concept of the virus carriers. This model has predicted the very accurate COVID-19 results at a mid-time of the lockdown period. Unfortunately, a good recovery rate was not achieved in Madhya Pradesh as expected by the model to stop the chain of virus spread. Thus, this novel model failed to predict the COVID-19 spread for a large duration. Nevertheless, this novel model has much potential to model the other parallel situations similar to COVID-19 spread.

scholarly journals Sensitifity Analysis of Mathematical Model of Coronavirus Disease (COVID-19) Transmission

CAUCHY ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 91 ◽  
Author(s):  
Resmawan Resmawan ◽  
Lailany Yahya
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Sensitivity Index ◽  
Contact Rate ◽  
Movement Rate ◽  
Exposed Individual ◽  
The Mathematical Model ◽  
Positive Index ◽  
Disease Free

<span class="fontstyle0">The study was aimed to introduce a new model construction regarding the transmission of Coronavirus Disease (henceforth, COVID-19) in human population. The mathematical model was constructed by taking into consideration several epidemiology parameters that are closely identical with the real condition. The study further conducted an analysis on the model by identifying the endemicity parameters of COVID-19, i.e., the presence of disease-free equilibrium (DFE) point and basic reproduction number. The next step was to carry out sensitivity analysis to find out which parameter is the most dominant to affect the disease’s endemicity. The results revealed that the parameters </span><span class="fontstyle2">𝜂, 𝜁</span><span class="fontstyle2">𝑠𝑒</span><span class="fontstyle2">, 𝛼,, </span><span class="fontstyle0">and </span><span class="fontstyle2">𝜎 </span><span class="fontstyle0">in sequence showed the most dominant sensitivity index towards the basic reproduction number. Moreover, the results indicated positive index in parameters </span><span class="fontstyle2">𝜂 </span><span class="fontstyle0">and </span><span class="fontstyle2">𝜁</span><span class="fontstyle2">𝑠𝑒 </span><span class="fontstyle0">that represented transmission chances during contact as well as contact rate between vulnerable individuals and exposed individual. This suggests that an<br />increase in the previous parameter value could potentially enlarge the endemicity of COVID-19. On the other hand, parameters </span><span class="fontstyle2">𝛼 </span><span class="fontstyle0">and </span><span class="fontstyle2">𝜎</span><span class="fontstyle0">, </span><span class="fontstyle0">representing movement rate of exposed<br />individuals to the quarantine class and proportion of quarantined exposed individuals, showed negative index. The numbers indicate that an increase in the parameter value could decrease the disease’s endemicity. All in all, the study concludes that treatments for COVID-19 should focus on<br />restriction of interaction between individuals and optimization of quarantine.</span> <br /><br />

scholarly journals Mathematical Modeling of Japanese Encephalitis under Aquatic Environmental Effects

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1880
Author(s):  
Faïçal Ndaïrou ◽  
Iván Area ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Japanese Encephalitis ◽  
Environmental Effects ◽  
Basic Reproduction Number ◽  
Local Stability ◽  
Reproduction Number ◽  
Well Posed ◽  
Disease Free ◽  
The Basic Reproduction Number

We propose a mathematical model for the spread of Japanese encephalitis with emphasis on the environmental effects on the aquatic phase of mosquitoes. The model is shown to be biologically well-posed and to have a biologically and ecologically meaningful disease-free equilibrium point. Local stability is analyzed in terms of the basic reproduction number and numerical simulations presented and discussed.

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

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