scholarly journals Measles dynamics on network models with optimal control strategies

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yuyi Xue ◽  
Xiaoe Ruan ◽  
Yanni Xiao
Keyword(s):  
Optimal Control ◽  
Transmission Rate ◽  
Control Strategies ◽  
Random Network ◽  
Network Models ◽  
Control Measures ◽  
Effective Control ◽  
Threshold Dynamics ◽  
Heterogeneous Model ◽  
Strong Control

AbstractTo 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 numerically find that the waning of immunity can lead to an increase in the basic reproduction number $R_{0}$ R 0 and the density of infected individuals. Moreover, there exists a critical level for average degree above which $R_{0}$ R 0 increases quicker in the scale-free network than in the random network. To design the effective control strategies for the subpopulations with different activities, we examine the optimal control problem of the heterogeneous model. Numerical studies suggest us no matter what the network is, we should implement control measures as soon as possible once the outbreak takes off, and particularly, the subpopulation with high connectivity should require high intensity of interventions. However, with delayed initiation of controls, relatively strong control measures should be given to groups with medium degrees. Furthermore, the allocation of costs (or resources) should coincide with their contact patterns.

scholarly journals Control Strategies for the Third wave of COVID-19 infection in India: A Mathematical Model Incorporating Vaccine Effectiveness

2022 ◽  
Author(s):  
Ashutosh Mahajan ◽  
Namitha Sivadas ◽  
Pooja Panda
Keyword(s):  
Transmission Rate ◽  
Control Strategies ◽  
Control Measures ◽  
Disease Spread ◽  
Effective Control ◽  
Third Wave ◽  
Social Distancing ◽  
Vaccination Rates ◽  
New Variant ◽  
The Future

The waning effectiveness of the COVID-19 vaccines and the emergence of a new variant Omicron has given rise to the possibility of another outbreak of the infection in India. COVID-19 has caused more than 34 million reported cases and 475 thousand deaths in India so far, and it has affected the country at the root level, socially as well as economically. After going through different control measures, mass vaccination has been achieved to a large extent for the highly populous country, and currently under progress. India has already been hit by a massive second wave of infection in April-June, 2021 mainly due to the delta variant, and might see a third wave in the near future that needs to be controlled with effective control strategies. In this paper, we present a compartmental epidemiological model with vaccinations incorporating the dose-dependent effectiveness. We study a possible sudden outbreak of SARS-CoV2 variants in the future, and bring out the associated predictions for various vaccination rates and point out optimum control measures. Our results show that for transmission rate 30% higher than the current rate due to emergence of new variant or relaxation of social distancing conditions, daily new cases can peak to 250k in March 2022, taking the second dose effectiveness dropping to 50% in the future. A combination of vaccination and controlled lockdown or social distancing is the key to tackling the current situation and for the coming few months. Our simulation results show that social distancing measures show better control over the disease spread than the higher vaccination rates. <br>

scholarly journals Analysis of Control Interventions against Malaria in communities with Limited Resources

2021 ◽  
Vol 29 (2) ◽  
pp. 71-91
Author(s):  
E.A. Bakare ◽  
B.O. Onasanya ◽  
S. Hoskova-Mayerova ◽  
O. Olubosede
Keyword(s):  
Optimal Control ◽  
Malaria Transmission ◽  
Control Strategies ◽  
Indoor Residual Spraying ◽  
Control Measures ◽  
Limited Resources ◽  
Effective Control ◽  
Bed Nets ◽  
Multiple Control ◽  
Potential Impact

Abstract The aim of this paper is to analyse the potential impact of multiple current interventions in communities with limited resources in order to obtain optimal control strategies and provide a basis for future predictions of the most effective control measures against the spread of malaria. We developed a population-based model of malaria transmission dynamics to investigate the effectiveness of five different interventions. The model captured both the human and the mosquito compartments. The control interventions considered were: educational campaigns to mobilise people for diagnostic test and treatment and to sleep under bed nets; treatment through mass drug administration; indoor residual spraying(IRS) with insecticide to reduce malaria transmission; insecticide treated net (ITN) to reduce morbidity; and regular destruction of mosquito breeding sites to reduce the number of new mosquito and bites/contact at dusks and dawn. Analysis of the potential impact of the multiple control interventions were carried out and the optimal control strategies that minimized the number of infected human and mosquito and the cost of applying the various control interventions were determined.

scholarly journals Control Strategies for the Third wave of COVID-19 infection in India: A Mathematical Model Incorporating Vaccine Effectiveness

2021 ◽  
Author(s):  
Namitha A Sivadas ◽  
Ashutosh Mahajan ◽  
Pooja Panda
Keyword(s):  
Transmission Rate ◽  
Control Strategies ◽  
Control Measures ◽  
Disease Spread ◽  
Effective Control ◽  
Third Wave ◽  
Social Distancing ◽  
Vaccination Rates ◽  
New Variant ◽  
The Future

The waning effectiveness of the COVID-19 vaccines and the emergence of a new variant Omicron has given rise to the possibility of another outbreak of the infection in India. COVID-19 has caused more than 34 million reported cases and 475 thousand deaths in India so far, and it has affected the country at the root level, socially as well as economically. After going through different control measures, mass vaccination has been achieved to a large extent for the highly populous country, and currently under progress. India has already been hit by a massive second wave of infection in April-June, 2021 mainly due to the delta variant, and might see a third wave in the near future that needs to be controlled with effective control strategies. In this paper, we present a compartmental epidemiological model with vaccinations incorporating the dose-dependent effectiveness. We study a possible sudden outbreak of SARS-CoV2 variants in the future, and bring out the associated predictions for various vaccination rates and point out optimum control measures. Our results show that for transmission rate 30% higher than the current rate due to emergence of new variant or relaxation of social distancing conditions, daily new cases can peak to 250k in March 2022, taking the second dose effectiveness dropping to 50% in the future. Combination of vaccination and controlled lockdown or social distancing is the key to tackling the current situation and for the coming few months. Our simulation results show that social distancing measures show better control over the disease spread than the higher vaccination rates.

scholarly journals Control Strategies for the Third wave of COVID-19 infection in India: A Mathematical Model Incorporating Vaccine Effectiveness

2022 ◽  
Author(s):  
Ashutosh Mahajan ◽  
Namitha Sivadas ◽  
Pooja Panda
Keyword(s):  
Transmission Rate ◽  
Control Strategies ◽  
Control Measures ◽  
Disease Spread ◽  
Effective Control ◽  
Third Wave ◽  
Social Distancing ◽  
Vaccination Rates ◽  
New Variant ◽  
The Future

The waning effectiveness of the COVID-19 vaccines and the emergence of a new variant Omicron has given rise to the possibility of another outbreak of the infection in India. COVID-19 has caused more than 34 million reported cases and 475 thousand deaths in India so far, and it has affected the country at the root level, socially as well as economically. After going through different control measures, mass vaccination has been achieved to a large extent for the highly populous country, and currently under progress. India has already been hit by a massive second wave of infection in April-June, 2021 mainly due to the delta variant, and might see a third wave in the near future that needs to be controlled with effective control strategies. In this paper, we present a compartmental epidemiological model with vaccinations incorporating the dose-dependent effectiveness. We study a possible sudden outbreak of SARS-CoV2 variants in the future, and bring out the associated predictions for various vaccination rates and point out optimum control measures. Our results show that for transmission rate 30% higher than the current rate due to emergence of new variant or relaxation of social distancing conditions, daily new cases can peak to 250k in March 2022, taking the second dose effectiveness dropping to 50% in the future. A combination of vaccination and controlled lockdown or social distancing is the key to tackling the current situation and for the coming few months. Our simulation results show that social distancing measures show better control over the disease spread than the higher vaccination rates. <br>

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.

An experimental evaluation of conventional control measures against the sheep tick, Ixodes ricinus (L.) (Acari: Ixodidae). II. The dynamics of the tick-host interaction

1985 ◽  
Vol 75 (3) ◽  
pp. 501-518 ◽  
Author(s):  
Sarah E. Randolph ◽  
Gordon M. Steele
Keyword(s):  
Ixodes Ricinus ◽  
Control Method ◽  
Control Strategies ◽  
Stocking Density ◽  
Experimental Manipulation ◽  
Control Measures ◽  
Effective Control ◽  
Contact Rate ◽  
Host Interaction ◽  
Questing Ticks

AbstractThe experimental manipulation of separate, but originally identical, populations of Ixodes ricinus (L.) by applying three conventional tick control measures in different enclosures on naturally infested moorland in Wales allowed the elements of the tick-host interaction to be analysed quantitatively and the effectiveness of the control methods to be compared. From the relationship between the sheep stocking density and the numbers of questing ticks picked up by fortnightly blanket-dragging in each enclosure, the death rate of ticks during their activity season and the rate of contact between sheep and ticks were calculated. From this, it was possible to investigate the effect of different stocking densities on the feeding success of ticks. A major factor determining the much lower contact rate for larvae than for nymphs was the different spatial distribution of questing ticks, clumped for larvae and random for nymphs. The non-random use by sheep of the three different vegetation zones in the paddock resulted in the highest contact rate between sheep and ticks in the pasture area, but tick survival was apparently highest in the bog area. Combining these factors resulted in the prediction that the bracken area was the least favourable habitat for ticks. In the two enclosures where the sheep were not treated with acaricide the mean tick loads on the sheep were similar, but the lower overall use of the pasture by the sheep in the low stocking density enclosure (2/ha) resulted in slightly lower tick loads there compared with those in the high stocking density enclosure (4/ha). The numbers of ticks counted in the second year showed that pasture spelling was the most effective control method, acaricide treatment was less effective, and the benefits of halving the stocking density were marginal. The implications of these results for control strategies are discussed.

scholarly journals Prevention of Influenza Pandemic by Multiple Control Strategies

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Roman Ullah ◽  
Gul Zaman ◽  
Saeed Islam
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Antiviral Treatment ◽  
Cost Effective ◽  
Effective Control ◽  
Numerical Techniques ◽  
Multiple Control ◽  
Control Functions ◽  
Transmission Of Disease

We present the prevention of influenza pandemic by using multiple control functions. First, we adjust the control functions in the pandemic model, then we show the existence of the optimal control problem, and, by using both analytical and numerical techniques, we investigate cost-effective control effects for the prevention of transmission of disease. To do this, we use four control functions, the first one for increasing the effect of vaccination, the second one for the strategies to isolate infected individuals, and the last two for the antiviral treatment to control clinically infectious and hospitalization cases, respectively. We completely characterized the optimal control and compute the numerical solution of the optimality system by using an iterative method.

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 Estimating the Optimal Control of Zoonotic Visceral Leishmaniasis by the Use of a Mathematical Model

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Laila Massad Ribas ◽  
Vera Lucia Zaher ◽  
Helio Junji Shimozako ◽  
Eduardo Massad
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Visceral Leishmaniasis ◽  
Vector Control ◽  
Control Strategy ◽  
Control Strategies ◽  
Effective Control ◽  
Alternative Control ◽  
Alternative Strategies ◽  
Zoonotic Visceral Leishmaniasis

We argue that the strategy of culling infected dogs is not the most efficient way to control zoonotic visceral leishmaniasis (ZVL) and that, in the presence of alternative control strategies with better potential results, official programs of compulsory culling adopted by some countries are inefficient and unethical. We base our arguments on a mathematical model for the study of control strategies against ZVL, which allows the comparison of the efficacies of 5, alternative strategies. We demonstrate that the culling program, previously questioned on both theoretical and practical grounds is the less effective control strategy. In addition, we show that vector control and the use of insecticide-impregnated dog collars are, by far, more efficient at reducing the prevalence of ZVL in humans.

PREVENTING THE SPREAD OF SCHISTOSOMIASIS IN GHANA: POSSIBLE OUTCOMES OF INTEGRATED OPTIMAL CONTROL STRATEGIES

2017 ◽  
Vol 25 (04) ◽  
pp. 625-655 ◽  
Author(s):  
HONG ZHANG ◽  
PRINCE HARVIM ◽  
PAUL GEORGESCU
Keyword(s):  
Optimal Control ◽  
Large Scale ◽  
Control Strategies ◽  
Endemic Equilibrium ◽  
Control Measures ◽  
Dimensional System ◽  
Vector Population ◽  
Sanitation And Hygiene ◽  
The Stability ◽  
Manifold Theory

The goal of a future free from schistosomiasis in Ghana can be achieved through integrated strategies, targeting simultaneously several stages of the life cycle of the schistosome parasite. In this paper, the transmission of schistosomiasis is modeled as a multi-scale 12-dimensional system of ODEs that includes vector-host and within-host dynamics of infection. An explicit expression for the basic reproduction number [Formula: see text] is obtained via the next generation method, this expression being interpreted in biological terms, as well as in terms of reproductive numbers for each type of interaction involved. After discussing the stability of the disease-free equilibrium and the existence and uniqueness of the endemic equilibrium, the Center Manifold Theory is used to show that for values of [Formula: see text] larger than 1, but close to 1, the unique endemic equilibrium is locally asymptotically stable. A sensitivity analysis indicates that [Formula: see text] is most sensitive to the natural death rate of the vector population, while numerical simulations of optimal control strategies reveal that the most effective strategy for the control and possible elimination of schistosomiasis should combine sanitary measures (access to safe water, improved sanitation and hygiene education), large-scale treatment of infected population and vector control measures (via the use of molluscicides), for a significant amount of time.

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