scholarly journals Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Aristide G. Lambura ◽  
Gasper G. Mwanga ◽  
Livingstone Luboobi ◽  
Dmitry Kuznetsov
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Drug Administration ◽  
Mass Drug Administration ◽  
Helminth Infection ◽  
Reproduction Number ◽  
Control Strategies ◽  
Active Tuberculosis ◽  
Control Measures ◽  
The Impact

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

scholarly journals Modeling the Impact of Optimal Control Strategies on the Dynamics of Zika Virus Disease Using the Sterile Insect Technology

2020 ◽  
pp. 13-33
Author(s):  
Atokolo William ◽  
Akpa Johnson ◽  
Daniel Musa Alih ◽  
Olayemi Kehinde Samuel ◽  
C. E. Mbah Godwin
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Zika Virus ◽  
Human Population ◽  
Necessary Conditions ◽  
Virus Disease ◽  
Control Strategies ◽  
Control Measures ◽  
Optimal Control Strategy ◽  
The Impact

This work is aimed at formulating a mathematical model for the control of zika virus infection using Sterile Insect Technology (SIT). The model is extended to incorporate optimal control strategy by introducing three control measures. The optimal control is aimed at minimizing the number of Exposed human, Infected human and the total number of Mosquitoes in a population and as such reducing contacts between mosquitoes and human, human to human and above all, eliminates the population of Mosquitoes. The Pontryagin’s maximum principle was used to obtain the necessary conditions, find the optimality system of our model and to obtain solution to the control problem. Numerical simulations result shows that; reduction in the number of Exposed human population, Infected human population and reduction in the entire population of Mosquito population is best achieved using the optimal control strategy.

OPTIMAL CONTROL ANALYSIS OF THE EFFECT OF TREATMENT, ISOLATION AND VACCINATION ON HEPATITIS B VIRUS

2020 ◽  
Vol 28 (02) ◽  
pp. 351-376 ◽  
Author(s):  
MUHAMMAD ALTAF KHAN ◽  
SYED AZHAR ALI SHAH ◽  
SAIF ULLAH ◽  
KAZEEM OARE OKOSUN ◽  
MUHAMMAD FAROOQ
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Control Strategies ◽  
Control Measures ◽  
Hepatitis B Infection ◽  
Control Variables ◽  
Effect Of Treatment ◽  
The Basic Reproduction Number

Hepatitis B infection is a serious health issue and a major cause of deaths worldwide. This infection can be overcome by adopting proper treatment and control strategies. In this paper, we develop and use a mathematical model to explore the effect of treatment on the dynamics of hepatitis B infection. First, we formulate and use a model without control variables to calculate the basic reproduction number and to investigate basic properties of the model such as the existence and stability of equilibria. In the absence of control measures, we prove that the disease free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity. Also, using persistent theorem, it is shown that the infection is uniformly persistent, whenever the basic reproduction number is greater than unity. Using optimal control theory, we incorporate into the model three time-dependent control variables and investigate the conditions required to curtail the spread of the disease. Finally, to illustrate the effectiveness of each of the control strategies on disease control and eradication, we perform numerical simulations. Based on the numerical results, we found that the first two strategies (treatment and isolation strategy) and (vaccination and isolation strategy) are not very effective as a long term control or eradication strategy for HBV. Hence, we recommend that in order to effectively control the disease, all the control measures (isolation, vaccination and treatment) must be implemented at the same time.

TRANSMISSION DYNAMICS AND OPTIMAL CONTROL OF AN INFLUENZA MODEL WITH QUARANTINE AND TREATMENT

2012 ◽  
Vol 05 (03) ◽  
pp. 1260011 ◽  
Author(s):  
WEI-WEI SHI ◽  
YUAN-SHUN TAN
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Influenza Pandemic ◽  
Control Measures ◽  
Globally Asymptotically Stable ◽  
Number Formula ◽  
Parameter Values ◽  
The Impact ◽  
Disease Free

We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic reproduction number [Formula: see text], the disease-free equilibrium (DFE) is globally asymptotically stable, if [Formula: see text], the disease is uniformly persistent. The model is then extended to assess the impact of three anti-influenza control measures, precaution, quarantine and treatment, by re-formulating the model as an optimal control problem. We focus primarily on controlling disease with a possible minimal the systemic cost. Pontryagin's maximum principle is used to characterize the optimal levels of the three controls. Numerical simulations of the optimality system, using a set of reasonable parameter values, indicate that the precaution measure is more effective in reducing disease transmission than the other two control measures. The precaution measure should be emphasized.

scholarly journals The impact of community-wide, mass drug administration on aggregation of soil-transmitted helminth infection in human host populations

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Marleen Werkman ◽  
James E. Wright ◽  
James E. Truscott ◽  
William E. Oswald ◽  
Katherine E. Halliday ◽  
...  
Keyword(s):  
Drug Administration ◽  
Mass Drug Administration ◽  
Helminth Infection ◽  
Human Host ◽  
The Impact

scholarly journals Shortages of hospital beds exacerbate severity of COVID-19 outbreaks

2020 ◽  
Author(s):  
Weike Zhou ◽  
Aili Wang ◽  
Xia Wang ◽  
Robert A Cheke ◽  
Sanyi Tang
Keyword(s):  
Prevention And Control ◽  
Reproduction Number ◽  
Control Strategies ◽  
Threshold Value ◽  
Control Measures ◽  
Unknown Parameters ◽  
Health Authorities ◽  
Hospital Beds ◽  
And Control ◽  
The Impact

Abstract Background: The global outbreak of COVID-19 has caused worrying concern amongst the public and health authorities. The first and foremost problem that many countries face is a shortage of medical resources. The experience of Wuhan, China, in fighting against COVID-19 provides a model for other countries to learn from. Methods: We formulated a piecewise smooth model to describe the limitation of hospital beds, based on the transmission progression of COVID-19, and the strengthening prevention and control strategies implemented in Wuhan, China. We used data of the cumulative numbers of confirmed cases, cured cases and deaths in Wuhan city from 10 January to 20 March, 2020 to estimate unknown parameters and the effective reproduction number. Sensitivity analysis was conducted to investigate the impact of a shortage of hospital beds on the COVID-19 outbreak. Results: Even with strong prevention and control measures in Wuhan, slowing down of the supply rate, reducing the maximum capacity and delaying the intervention time of supplementing hospital beds aggravated the outbreak severity by magnifying the cumulative numbers of confirmed cases and deaths, prolonging the period of the outbreak in Wuhan, enlarging the value of the effective reproduction number during the outbreak and postponing the time when the threshold value is reduced to 1. Conclusions: The quick establishment of the Huoshenshan and Leishenshan Hospitals in a short time and the deployment of mobile cabin hospitals played important roles in containing the COVID-19 outbreak in Wuhan, providing a model for other countries to provide more hospital beds for COVID-19 patients faster and earlier.

scholarly journals Mathematical Model for Optimal Control of Soil-Transmitted Helminth Infection

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Aristide G. Lambura ◽  
Gasper G. Mwanga ◽  
Livingstone Luboobi ◽  
Dmitry Kuznetsov
Keyword(s):  
Optimal Control ◽  
Health Education ◽  
Basic Reproduction Number ◽  
Helminth Infection ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Control Measures ◽  
Personal Hygiene ◽  
Susceptible Population ◽  
The Basic Reproduction Number

In this paper, we study the dynamics of soil-transmitted helminth infection. We formulate and analyse a deterministic compartmental model using nonlinear differential equations. The basic reproduction number is obtained and both disease-free and endemic equilibrium points are shown to be asymptotically stable under given threshold conditions. The model may exhibit backward bifurcation for some parameter values, and the sensitivity indices of the basic reproduction number with respect to the parameters are determined. We extend the model to include control measures for eradication of the infection from the community. Pontryagian’s maximum principle is used to formulate the optimal control problem using three control strategies, namely, health education through provision of educational materials, educational messages to improve the awareness of the susceptible population, and treatment by mass drug administration that target the entire population(preschool- and school-aged children) and sanitation through provision of clean water and personal hygiene. Numerical simulations were done using MATLAB and graphical results are displayed. The cost effectiveness of the control measures were done using incremental cost-effective ratio, and results reveal that the combination of health education and sanitation is the best strategy to combat the helminth infection. Therefore, in order to completely eradicate soil-transmitted helminths, we advise investment efforts on health education and sanitation controls.

scholarly journals Dynamics of individual adherence to mass drug administration in a conditional probability model

2020 ◽  
Author(s):  
Robert J. Hardwick ◽  
James E. Truscott ◽  
William E. Oswald ◽  
Marleen Werkman ◽  
Katherine E. Halliday ◽  
...  
Keyword(s):  
Drug Administration ◽  
Mass Drug Administration ◽  
Real World ◽  
Disease Transmission ◽  
Neglected Tropical Diseases ◽  
Probability Model ◽  
Control Measures ◽  
Real World Data ◽  
Adherence Behaviour ◽  
The Impact

AbstractWe present a comprehensive framework which describes the systematic (binary) choice of individuals to either take treatment, or not for any reason, over the course of multiple rounds of mass drug administration (MDA) — which we here here refer to as ‘adherence’ and ‘non-adherence’. This methodology can be fitted to (or informed by) program data as well as manipulated to reproduce the same adherence behaviours of past analyses, and can go beyond past analyses to describe new behaviours that have yet to be considered in the literature. Our model also has a straightforward interpretation and implementation in simulations of mass drug trials for disease transmission studies and forecasts for control through MDA. We demonstrate how our analysis may be implemented to statistically infer adherence behaviour from a dataset by applying our approach to the recent adherence data from the TUMIKIA project, a recent trial of deworming strategies in Kenya. We stratify our analysis according to age and sex, though the framework which we introduce here may be readily adapted to accomodate other categories. Our findings include the detection of past behaviour dependent non-adherence in all age groups to varying degrees of severity and particularly strong non-adherent behaviour of men of ages 30+. We then demonstrate the use of our model in stochastic individual-based simulations by running two example forecasts for elimination in TUMIKIA with the learned adherence behaviour implemented. Our results demonstrate the impact and utility of including non-adherence from real world datasets in simulations.Author summaryMass drug administration (MDA) is an important tool in prevention of morbidity from various neglected tropical diseases (NTDs). Due to a variety of social and medical reasons, many people will either not be offered or refuse such treatment, and if this behaviour is recurring then control measures may face a challenge to achieving their stated goals. Learning the patterns of individual adherence or non-adherence to MDA control measures for NTDs from real world data followed by their implementation in simulated scenarios is a relatively recent development in the study of NTDs. Past analyses assessing individual adherence have informed the approach we take in this work. However, we have sought to provide a framework which encapsulates as many types of adherence behaviour as possible so that their implementation in modern simulations is streamlined effectively. Our example application to the TUMIKIA data highlights the importance of such a general framework as we find past behaviour dependence that may have been missed by other methods.

scholarly journals Transmission dynamics and high infectiousness of Coronavirus Disease 2019

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Shunxiang Huang ◽  
Lin Wu ◽  
Jing Li ◽  
Ming-Zhen Xin ◽  
Yingying Wang ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
Development Trend ◽  
Asymptomatic Infection ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Natural State ◽  
Global Public Health ◽  
Natural Reproduction ◽  
The Impact

<p style='text-indent:20px;'>Coronavirus disease 2019 (COVID-19) has rapidly spread around the world since the early 2020. Recently, a second wave of COVID-19 has resurged in many countries. The transmission dynamics and infectiousness of the COVID-19 pandemic remain unclear, and developing strategies to mitigate the severity of the pandemic is a top priority for global public health. According to the infection mechanism of COVID-19, a novel susceptible-asymptomatic-symptomatic-recovered (SASR) model with control variables in a patchy environment was proposed not only to consider the key characteristics of asymptomatic infection and the effects of seasonal variation but also to incorporate different control measures for multiple transmission routes. The basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ R_{0} $\end{document}</tex-math></inline-formula> was established to describe the spreading behavior in the natural state over a long time horizon, and the natural reproduction number <inline-formula><tex-math id="M2">\begin{document}$ R_{n} $\end{document}</tex-math></inline-formula>, which describes the development trend of the disease during a short time in the future, was defined according to the actual propagation characteristics. In addition, the effective reproduction number <inline-formula><tex-math id="M3">\begin{document}$ R_{e} $\end{document}</tex-math></inline-formula> considering the control strategies was proposed to evaluate the impact of non-pharmaceutical interventions. The results of numerical simulations for COVID-19 cases in Wuhan, China, based on the SASR model indicate that <inline-formula><tex-math id="M4">\begin{document}$ R_{0} $\end{document}</tex-math></inline-formula> was 3.58, <inline-formula><tex-math id="M5">\begin{document}$ R_{n} $\end{document}</tex-math></inline-formula> ranged from 2.37 to 4.91, and <inline-formula><tex-math id="M6">\begin{document}$ R_{e} $\end{document}</tex-math></inline-formula> decreased gradually from 4.83 on December 8, 2019 to 0.31 on March 8, 2020, reaching 1.40 on January 23, 2020, when the lockdown was lifted in Wuhan. We further concluded that the total number of infections, including asymptomatic infections, was approximately 301, 804 as of March 8, 2020, in Wuhan, China. In particular, this article proposes a dynamic method to distinguish the impact of natural factors and human interventions on the development of the pandemic, and provides a theoretical basis for fighting the global COVID-19 pandemic.</p>

scholarly journals Feasibility of onchocerciasis elimination using a “test-and-not-treat” strategy in Loa loa co-endemic areas

2020 ◽  
Author(s):  
David J Blok ◽  
Joseph Kamgno ◽  
Sebastien D Pion ◽  
Hugues C Nana-Djeunga ◽  
Yannick Niamsi-Emalio ◽  
...  
Keyword(s):  
Adverse Events ◽  
Drug Administration ◽  
Mass Drug Administration ◽  
Treatment Duration ◽  
Loa Loa ◽  
Serious Adverse Events ◽  
Endemic Areas ◽  
The Individual ◽  
The Impact ◽  
Main Strategy

Abstract Background Mass drug administration (MDA) with ivermectin is the main strategy for onchocerciasis elimination. Ivermectin is generally safe but associated with serious adverse events in individuals with high Loa loa microfilarial densities (MFD). Therefore, ivermectin MDA is not recommended in areas where onchocerciasis is hypo-endemic and L. loa is co-endemic. To eliminate onchocerciasis in those areas, a test-and-not-treat (TaNT) strategy has been proposed. We investigated whether onchocerciasis elimination can be achieved using TaNT and the required duration. Methods We used the individual-based model ONCHOSIM to predict the impact of TaNT on onchocerciasis microfilarial (mf) prevalence. We simulated pre-control mf prevalence levels from 2-40%. The impact of TaNT was simulated under varying levels of participation, systematic non-participation and exclusion from ivermectin due to high L. loa MFD. For each scenario, we assessed the time to elimination, defined as bringing onchocerciasis mf prevalence below 1.4%. Results In areas with 30-40% pre-control mf prevalence, the model predicted that it would take between 14 and 16 years to bring the mf prevalence below 1.4% using conventional MDA, assuming 65% participation. TaNT would increase the time to elimination by up to 1.5 years, depending on the level of systematic non-participation and the exclusion rate. At lower exclusion rates (≤2.5%), the delay would be less than six months. Conclusions Our model predicts that onchocerciasis can be eliminated using TaNT in L. loa co-endemic areas. The required treatment duration using TaNT would be only slightly longer than in areas with conventional MDA, provided that participation is good.

scholarly journals The impact of mass drug administration expansion to low onchocerciasis prevalence settings in case of connected villages

2021 ◽  
Vol 15 (5) ◽  
pp. e0009011
Author(s):  
Anneke S. de Vos ◽  
Wilma A. Stolk ◽  
Luc E. Coffeng ◽  
Sake J. de Vlas
Keyword(s):  
Intermediate Host ◽  
Drug Administration ◽  
Mass Drug Administration ◽  
Human Populations ◽  
Individual Based Model ◽  
Low Prevalence ◽  
The Impact ◽  
Local Transmission

Background The existence of locations with low but stable onchocerciasis prevalence is not well understood. An often suggested yet poorly investigated explanation is that the infection spills over from neighbouring locations with higher infection densities. Methodology We adapted the stochastic individual based model ONCHOSIM to enable the simulation of multiple villages, with separate blackfly (intermediate host) and human populations, which are connected through the regular movement of the villagers and/or the flies. With this model we explore the impact of the type, direction and degree of connectedness, and of the impact of localized or full-area mass drug administration (MDA) over a range of connected village settings. Principal findings In settings with annual fly biting rates (ABR) below the threshold needed for stable local transmission, persistence of onchocerciasis prevalence can well be explained by regular human traffic and/or fly movement from locations with higher ABR. Elimination of onchocerciasis will then theoretically be reached by only implementing MDA in the higher prevalence area, although lingering infection in the low prevalence location can trigger resurgence of transmission in the total region when MDA is stopped too soon. Expanding MDA implementation to the lower ABR location can therefore shorten the duration of MDA needed. For example, when prevalence spill-over is due to human traffic, and both locations have about equal populations, then the MDA duration can be shortened by up to three years. If the lower ABR location has twice as many inhabitants, the reduction can even be up to six years, but if spill-over is due to fly movement, the expected reduction is less than a year. Conclusions/Significance Although MDA implementation might not always be necessary in locations with stable low onchocerciasis prevalence, in many circumstances it is recommended to accelerate achieving elimination in the wider area.

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