Number Of Susceptible Individuals Research Articles

Two-Age-Structured COVID-19 Epidemic Model: Estimation of Virulence Parameters through New Data Incorporation

The COVID-19 epidemic has required countries to implement different containment strategies to limit its spread, like strict or weakened national lockdown rules and the application of age-stratified vaccine prioritization strategies. These interventions have in turn modified the age-dependent patterns of social contacts. In our recent paper, starting from the available age-structured real data at the national level, we identified, for the Italian case, specific virulence parameters for a two-age-structured COVID-19 epidemic compartmental model (under 60, and 60 years and over) in six different diseases transmission scenarios under concurrently adopted feedback interventions. An interpretation of how each external scenario modifies the age-dependent patterns of social contacts and the spread of COVID-19 disease has been accordingly provided. In this paper, which can be viewed as a sequel to the previous one, we mainly apply the same general methodology therein (involving the same dynamic model) to new data covering the three subsequent additional scenarios: (i) a mitigated coordinated intermittent regional action in conjunction with the II vaccination phase; (ii) a super-attenuated coordinated intermittent regional action in conjunction with the II vaccination phase; and (iii) a last step towards normality in conjunction with the start of the III vaccination phase. As a new contribution, we show how meaningful updated information can be drawn out, once the identification of virulence parameters, characterizing the two age groups within the latest three different phases, is successfully carried out. Nevertheless, differently from our previous paper, the global optimization procedure is carried out here with the number of susceptible individuals in each scenario being left free to change, to account for reinfection and immunity due to vaccination. Not only do the slightly different estimates we obtain for the previous scenarios not impact any of the previous considerations (and thus illustrate the robustness of the procedure), but also, and mainly, the new results provide a meaningful picture of the evolution of social behaviors, along with the goodness of strategic interventions.

Mathematical modeling of cholera dynamics with intrinsic growth considering constant interventions

A mathematical model that describes the dynamics of bacterium vibrio cholera within a fixed population considering intrinsic bacteria growth, therapeutic treatment, sanitation and vaccination rates is developed. The developed mathematical model is validated against real cholera data. A sensitivity analysis of some of the model parameters is also conducted. The intervention rates are found to be very important parameters in reducing the values of the basic reproduction number. The existence and stability of equilibrium solutions to the mathematical model are also carried out using analytical methods. The effect of some model parameters on the stability of equilibrium solutions, number of infected individuals, number of susceptible individuals and bacteria density is rigorously analyzed. One very important finding of this research work is that keeping the vaccination rate fixed and varying the treatment and sanitation rates provide a rapid decline of infection. The fourth order Runge–Kutta numerical scheme is implemented in MATLAB to generate the numerical solutions.

Sliding dynamics and bifurcations of a human influenza system under logistic source and broken line control strategy.

This paper proposes a non-smooth human influenza model with logistic source to describe the impact on media coverage and quarantine of susceptible populations of the human influenza transmission process. First, we choose two thresholds $ I_{T} $ and $ S_{T} $ as a broken line control strategy: Once the number of infected people exceeds $ I_{T} $, the media influence comes into play, and when the number of susceptible individuals is greater than $ S_{T} $, the control by quarantine of susceptible individuals is open. Furthermore, by choosing different thresholds $ I_{T} $ and $ S_{T} $ and using Filippov theory, we study the dynamic behavior of the Filippov model with respect to all possible equilibria. It is shown that the Filippov system tends to the pseudo-equilibrium on sliding mode domain or one endemic equilibrium or bistability endemic equilibria under some conditions. The regular/virtulal equilibrium bifurcations are also given. Lastly, numerical simulation results show that choosing appropriate threshold values can prevent the outbreak of influenza, which implies media coverage and quarantine of susceptible individuals can effectively restrain the transmission of influenza. The non-smooth system with logistic source can provide some new insights for the prevention and control of human influenza.

Vaccine allocation policy optimization and budget sharing mechanism using reinforcement learning

The optimal allocation of vaccines to population subgroups over time is a challenging health care management problem. In the context of a pandemic, the interaction between vaccination policies adopted by multiple agents and their cooperation (or lack thereof) creates a complex environment that affects the global transmission dynamics of the disease. In this study, we take the perspective of decision-making agents that aim to minimize the size of their susceptible populations and must allocate vaccines under limited supply. We assume that vaccine efficiency rates are unknown to agents and we propose a reinforcement learning approach based on Thompson sampling to learn the mean vaccine efficiency rates over time. Furthermore, we develop a budget-balanced resource sharing mechanism to promote cooperation among agents. We apply the proposed framework to the COVID-19 pandemic. We use a raster model of the world where agents represent the main countries worldwide and interact in a global mobility network to generate multiple problem instances. Our numerical results show that the proposed vaccine allocation policy achieves a larger reduction in the number of susceptible individuals, infections and deaths globally compared to a population-based policy. In addition, we show that, under a fixed global vaccine allocation budget, most countries can reduce their national number of infections and deaths by sharing their budget with countries with which they have a relatively high mobility exchange. The proposed framework can be used to improve policy-making in health care management by national and global health authorities.

Ulusal aşı programı ve kitlesel göçün, 2013-2018 arasında çocuklarda hepatit A epidemiyolojisine etkileri

Aim: Acute hepatitis A is a common public health problem in underdeveloped and developing countries. The hepatitis A vaccine was implemented as part of the National Immunization Program in Turkey in November 2012. The present study aimed to investigate the effects of the national vaccination program and massive migration on the epidemiology and clinical burden of hepatitis A infection.
 Material and Method: The study was a single center, retrospective chart review study among children diagnosed with viral hepatitis A infection between 0 and 18 years of age from January 2013 to February 2018 in Gaziantep Cengiz Gökçek Maternity and Children Hospital, Turkey. All cases’ age, diagnosis time, nationality, and gender information were evaluated. The length of stay, the maximum value of alanine transaminase and aspartate aminotransferase, and the direct medical cost of hospitalization were also evaluated in hospitalized cases.
 Results: During the study period total of 1039 cases were diagnosed with hepatitis A infection. Of these cases, 53% were males, 14% were Syrian refugees, and the median age was 7.9-year. The number of cases per year (2013 through 2017) was 321, 360, 157, 119, and 73, respectively. The majority of the cases were detected in November, December, and January. While the total number of cases was declining, we saw that the number of Syrian cases was increasing. The percentage of Syrian children in total cases in 2013 and 2017 was 6.5% and 52.1%, respectively. The hospitalization rate was %49.4, the median length of stay was four days, and the average medical cost of hospitalization was 246.8$/case.
 Conclusion: With the national vaccination program, prevalence is declining, but the number of susceptible individuals in society is still adversely affecting the epidemiology of the disease. Continuous monitoring of epidemiological data and efforts to expand vaccine coverage are required for infection control.

Modeling scenarios for mitigating outbreaks in congregate settings.

The explosive outbreaks of COVID-19 seen in congregate settings such as prisons and nursing homes, has highlighted a critical need for effective outbreak prevention and mitigation strategies for these settings. Here we consider how different types of control interventions impact the expected number of symptomatic infections due to outbreaks. Introduction of disease into the resident population from the community is modeled as a stochastic point process coupled to a branching process, while spread between residents is modeled via a deterministic compartmental model that accounts for depletion of susceptible individuals. Control is modeled as a proportional decrease in the number of susceptible residents, the reproduction number, and/or the proportion of symptomatic infections. This permits a range of assumptions about the density dependence of transmission and modes of protection by vaccination, depopulation and other types of control. We find that vaccination or depopulation can have a greater than linear effect on the expected number of cases. For example, assuming a reproduction number of 3.0 with density-dependent transmission, we find that preemptively reducing the size of the susceptible population by 20% reduced overall disease burden by 47%. In some circumstances, it may be possible to reduce the risk and burden of disease outbreaks by optimizing the way a group of residents are apportioned into distinct residential units. The optimal apportionment may be different depending on whether the goal is to reduce the probability of an outbreak occurring, or the expected number of cases from outbreak dynamics. In other circumstances there may be an opportunity to implement reactive disease control measures in which the number of susceptible individuals is rapidly reduced once an outbreak has been detected to occur. Reactive control is most effective when the reproduction number is not too high, and there is minimal delay in implementing control. We highlight the California state prison system as an example for how these findings provide a quantitative framework for understanding disease transmission in congregate settings. Our approach and accompanying interactive website (https://phoebelu.shinyapps.io/DepopulationModels/) provides a quantitative framework to evaluate the potential impact of policy decisions governing infection control in outbreak settings.

Estimates of the collective immunity to COVID-19 derived from a stochastic cellular automaton based framework.

In the context of the propagation of infectious diseases, when a sufficient degree of immunisation is achieved within a population, the spread of the disease is ended or significantly decreased, leading to collective immunity, meaning the indirect protection given by immune individuals to susceptible individuals. Here we describe the estimates of the collective immunity to COVID-19 from a stochastic cellular automaton based model designed to emulate the spread of SARS-CoV-2 in a population of static individuals interacting only via a Moore neighbourhood of radius one, with a view to analyze the impact of initially immune individuals on the dynamics of COVID-19. This impact was measured by comparing a progression of initial immunity ratio—the percentage of immunised individuals before patient zero starts infecting its neighbourhood—from 0 to 95% of the initial population, with the number of susceptible individuals not contaminated, the peak value of active cases, the total number of deaths and the emulated pandemic duration in days. The influence of this range of immunities over the model was tested with different parameterisations regarding the uncertainties involved in the model such as the durations of the cellular automaton states, the contamination contributions of each state and the state transition probabilities. A collective immunity threshold of 55% pm 2.5% on average was obtained from this procedure, under four distinct parameterisations, which is in tune with the estimates of the currently available medical literature, even increasing the uncertainty of the input parameters.

Transmission dynamics of varicella before, during and after the COVID-19 pandemic in Japan: a modelling study.

Public health and social measures (PHSMs) targeting the coronavirus disease 2019 (COVID-19) pandemic have potentially affected the epidemiological dynamics of endemic infectious diseases. In this study, we investigated the impact of PHSMs for COVID-19, with a particular focus on varicella dynamics in Japan. We adopted the susceptible-infectious-recovered type of mathematical model to reconstruct the epidemiological dynamics of varicella from Jan. 2010 to Sep. 2021. We analyzed epidemiological and demographic data and estimated the within-year and multi-year component of the force of infection and the biases associated with reporting and ascertainment in three periods: pre-vaccination (Jan. 2010-Dec. 2014), pre-pandemic vaccination (Jan. 2015-Mar. 2020) and during the COVID-19 pandemic (Apr. 2020-Sep. 2021). By using the estimated parameter values, we reconstructed and predicted the varicella dynamics from 2010 to 2027. Although the varicella incidence dropped drastically during the COVID-19 pandemic, the change in susceptible dynamics was minimal; the number of susceptible individuals was almost stable. Our prediction showed that the risk of a major outbreak in the post-pandemic era may be relatively small. However, uncertainties, including age-related susceptibility and travel-related cases, exist and careful monitoring would be required to prepare for future varicella outbreaks.

Predicting the Death Rate Around the World Due to COVID-19 Using Regression Analysis

Nowadays, COVID-19 is considered to be the biggest disaster that the world is facing. It has created a lot of destruction in the whole world. Due to this COVID-19, analysis has been done to predict the death rate and infected rate from the total population. To perform the analysis on COVID-19, regression analysis has been implemented by applying the differential equation and ordinary differential equation (ODE) on the parameters. The parameters taken for analysis are the number of susceptible individuals, the number of Infected Individuals, and the number of Recovered Individuals. This work will predict the total cases, death cases, and infected cases in the near future based on different reproductive rate values. This work has shown the comparison based on 4 different productive rates i.e. 2.45, 2.55, 2.65, and 2.75. The analysis is done on two different datasets; the first dataset is related to China, and the second dataset is associated with the world's data. The work has predicted that by 2020-08-12: 59,450,123 new cases and 432,499,003 total cases and 10,928,383 deaths.

Global control of COVID-19: good vaccines may not suffice

ABSTRACTThe COVID-19 pandemic has unveiled health and socioeconomic inequities around the globe. Effective epidemic control requires the achievement of herd immunity, where susceptible individuals are conferred indirect protection by being surrounded by immunized individuals. The proportion of people that need to be vaccinated to obtain herd immunity is determined through the herd immunity threshold. However, the number of susceptible individuals and the opportunities for contact between infectious and susceptible individuals influence the progress of an epidemic. Thus, in addition to vaccination, control of a pandemic may be difficult or impossible to achieve without other public health measures, including wearing face masks and social distancing. This article discusses the factors that may contribute to herd immunity and control of COVID-19 through the availability of effective vaccines and describes how vaccine effectiveness in the community may be lower than that expected. It also discusses how pandemic control in some countries and populations may face vaccine accessibility barriers if market forces strongly regulate the new technologies available, according to the inverse care law.

Assessing Changes in the Reproduction Number of COVID-19 in Cameroon

Aim: The purpose of this work is to assess changes that occur on COVID-19 infection in Cameroon since the start of the epidemic.
 Study Design: We use a data-based analysis on longitudinal data of reported COVID-19 cases in Cameroon.
 Place and Duration: The data for the study were obtained from the reports of confirmed COVID-19 cases from an official website between March 7, 2020 to September 29, 2021.
 Methodology: A modified Susceptible-Infected-Recovered-Deceased (SIRD) model for the contagion was used to describe the cumulated cases of COVID-19 during different phases of the epidemic that correlated with highest spikes. The approach features several aspects: one is that model parameters can be time-varying, allowing us to capture possible changes of the epidemic behaviour, due for example to containment measures enforced by authorities or modifications of the epidemic characteristics, country events, and COVID-19 vaccine introduction; the second aspect is that the model accounts for a social distancing parameter. The time-varying parameters was handled using a phase-to-phase modelling in which initial parameters were the number of susceptible individuals at the end of each phase. In addition, daily incidence data were used to estimate daily reproduction number. Secondly, we used an Autoregressive Integrated Moving Average (ARIMA) approach to analyse the dynamic of the effective reproduction number R and forecast the new number of infected contacts.
 Results: There was less than 54% compliance of social distancing during all phases. The reproduction number was above 1 during each phase of the analysis. As of September 2021, it was 2.43 suggesting a constant increase of infection. Time-series of the reproduction number was unseasonal and stationary. Forecasting of R gave a value of more than 2, suggesting a continued rise in the number of infected cases in the Country in the next coming months.
 Conclusion: It is uncertain when the pandemic will last in the country. While social distancing is in decrease, prevention through vaccination is an option to reach more people and stop the propagation of the disease.

Mathematical modeling of transmission dynamics of COVID-19

<abstract> The emergence of coronavirus disease 2019 (COVID-19) demonstrates the importance of research on understanding and accurately modeling the transmission and spread of pandemic. In this paper, we consider a susceptible-exposed-infected-recovered-deceased (SEIRD) system of differential equations to describe relationship among the number of susceptible individuals, the number of exposed individuals who are transmitting the virus, the number of infected individuals among the exposed people, the number of recovered individuals from those infected, and the number of deaths from those infected in a town, state or country. Based on the empirical results of transmission process of COVID-19 in the United States from April 16th to June 30th, 2020, we consider a few cases of contact rate, incidence rate, recovery rate, and mortality rate to model the transmission and dynamics of the virus. Numerical analysis and analytical method are used to explore the dynamics and prediction of the pandemic. </abstract>

Herd immunity: In relation to COVID-19

Herd immunity, also known as indirect protection, community immunity, or community protection, refers to the protection of susceptible individuals against an infection when a sufficiently large proportion of immune individuals exist in a population. In other words, herd immunity is the inability of infected individuals to propagate an epidemic outbreak due to lack of contact with sufficient numbers of susceptible individuals. It stems from the individual immunity that may be gained through natural infection or through vaccination. The term herd immunity was initially introduced more than a century ago. In the latter half of the 20th century, the use of the term became more prevalent with the expansion of immunization programs and the need for describing targets for immunization coverage, discussions on disease eradication, and cost-effectiveness analyses of vaccination programs. Eradication of smallpox and sustained reductions in disease incidence in adults and those who are not vaccinated following routine childhood immunization with conjugated Haemophilusinfluenzae type B and pneumococcal vaccines are successful examples of the effects of vaccine-induced herd immunity.

An Analysis of the Italian Lockdown in Retrospective Using Particle Swarm Optimization in Machine Learning Applied to an Epidemiological Model

A critical analysis of the open data provided by the Italian Civil Protection Centre during phase 1 of Covid-19 epidemic—the so-called Italian lockdown—is herein proposed in relation to four of the most affected Italian regions, namely Lombardy, Reggio Emilia, Valle d’Aosta, and Veneto. A possible bias in the data induced by the extent in the use of medical swabs is found in relation to Valle d’Aosta and Veneto. Observed data are then interpreted using a Susceptible-Infectious-Recovered (SIR) epidemiological model enhanced with asymptomatic (infected and recovered) compartments, including lockdown effects through time-dependent model parameters. The initial number of susceptible individuals for each region is also considered as a parameter to be identified. The issue of parameters identification is herein addressed by a robust machine learning approach based on particle swarm optimization. Model predictions provide relevant information for policymakers in terms of the effect of lockdown measures in the different regions. The number of susceptible individuals involved in the epidemic, important for a safe release of lockdown during the next phases, is predicted to be around 10% of the population for Lombardy, 16% for Reggio Emilia, 18% for Veneto, and 40% for Valle d’Aosta.

A Primer on COVID‐19 Mathematical Models

The emergence of severe acute respiratory syndrome coronavirus 2 (or coronavirus disease [COVID]-19) has led to a widespread global pandemic ((1)). COVID-19 symptoms and mortality are disproportionately more severe in people with obesity and obesity-related comorbidities ((2, 3)). This is of concern for the United States, where ~42% have obesity, and of these, 85% have type 2 diabetes. Without effective vaccines or therapies, there is an urgent need for prevention and treatment strategies for COVID-19 infections. Developing such strategies requires a thorough understanding of how COVID-19 infections spread in a population. Mathematical modeling predicts the spread of COVID-19 and permits testing different strategies to control and reduce population disease impacts. The New York Times published COVID-19 predictions from five mathematical models with widely varying results ((4)). A recent review ((5)) also highlighted model differences and noted that a fluid situation dependent on many external variables should not be viewed as a “crystal ball.” Why do COVID-19 models yield such variable predictions? How are the different COVID-19 models developed? How should models be applied? Here, we provide a brief tutorial addressing these questions. The majority of models fall into the following two categories, which are applied for different purposes: projections versus statistical forecasts. Projections are deterministic and they explain what could happen under a set of underlying hypotheses, while statistical forecasts use observed data to predict what will happen ((6)). In 1927, Kermack and McKendrick ((7)) developed the first continuous variable projection model of epidemic population dynamics, often referred to as a “susceptible, infected, and removed” (SIR) model. They compartmentalized a constant population into three states. The first state represents individuals susceptible to the disease with the number of susceptible individuals on day of the epidemic, denoted by The second state is the number of infected individuals on day of the epidemic, denoted by Finally, individuals removed from the infectious disease dynamics through death or recovery with immunity on day of the epidemic are denoted by The key property of projection models like the Kermack-McKendrick system is that they are based on logical assumptions of the underlying mechanics of a process and they can be developed without data to immediately address “what if” questions. Here, r declines as the number of infected individuals gets higher, reflecting increased social distancing during peak infectivity. On the other hand, increases when the number of infected individuals decrease. The values , K, and n are parameters that could be fit to data once available. The changes in assumptions alter the projections as depicted in Figure 2. Once data is fit to model parameters, SIR models can predict when infections peak or how high the peak may be, but as pointed out in Jewell et al. ((5)) and observed in Figure 2, these are dependent on the underlying model assumptions. Forecasting models are more useful after data has been gathered. For instance, most SIR COVID-19 models use fixed parameters, which lead to a constant referred to as or “ naught.” is defined as the number of secondary infections that will result from a single infected individual being introduced into a completely susceptible population. A calculated reproduction number during an ongoing epidemic is the “effective” reproduction number, , which is the observed average number of secondary cases from a single primary case per unit time. accounts for changes to through control measures such as social distancing. Within the SIR framework, , where is the time to recover and is the population size. Absent of interventions, the estimated of COVID-19 is between 1.5 and 6.7 ((9)). However, this value is not constant but changing daily. Renewal equations allow us to estimate values ((10)) of that can be fit to a statistical model. Similar to Massad et al. ((6)), we fit an exponential decay model to New York’s data yielding , though other statistical models such as one with an asymptote could be considered. Figure 3 depicts the fitted effective reproduction number versus the calculated values for New York. This forecast model will inform improved SIR model projections and generate prediction intervals. Projection models for the SARS-1 epidemic overestimate compared with statistical forecasting estimates of reproduction numbers ((6)). It is important that researchers use projection models for hypothetical scenario development and statistical forecasting models for forecasting, which are two different goals. Including the differential effects of COVID-19 on individuals with obesity into both projection and forecasting models by separating each compartment into normal weight and obesity populations will be key to understanding the population-wide impacts of COVID-19 on obesity. Obesity researchers can apply both types of models to evaluate prevention and treatment strategies for COVID-19 in persons with obesity.

A SIR model assumption for the spread of COVID-19 in different communities.

In this paper, we study the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop a susceptible-infected-removed (SIR) model that provides a theoretical framework to investigate its spread within a community. Here, the model is based upon the well-known susceptible-infected-removed (SIR) model with the difference that a total population is not defined or kept constant per se and the number of susceptible individuals does not decline monotonically. To the contrary, as we show herein, it can be increased in surge periods! In particular, we investigate the time evolution of different populations and monitor diverse significant parameters for the spread of the disease in various communities, represented by China, South Korea, India, Australia, USA, Italy and the state of Texas in the USA. The SIR model can provide us with insights and predictions of the spread of the virus in communities that the recorded data alone cannot. Our work shows the importance of modelling the spread of COVID-19 by the SIR model that we propose here, as it can help to assess the impact of the disease by offering valuable predictions. Our analysis takes into account data from January to June, 2020, the period that contains the data before and during the implementation of strict and control measures. We propose predictions on various parameters related to the spread of COVID-19 and on the number of susceptible, infected and removed populations until September 2020. By comparing the recorded data with the data from our modelling approaches, we deduce that the spread of COVID-19 can be under control in all communities considered, if proper restrictions and strong policies are implemented to control the infection rates early from the spread of the disease.

A two-thresholds policy for a Filippov model in combating influenza

This work designs a two-thresholds policy for a Filippov model in combating influenza, so as to estimate when and whether to take control strategies, including the media coverage, antiviral treatment of infected individuals and vaccination of susceptible population. By introducing two tolerance thresholds [Formula: see text] and [Formula: see text] of susceptible and infected individuals, the two-thresholds policy is designed as: a vaccination program is implemented when the number of susceptible individuals is above [Formula: see text]; an antiviral treatment strategy is taken and the mass media begins to report information about influenza when the infection number is larger than [Formula: see text]; no control strategies are required in other cases. Furthermore, the global dynamics of the model are analyzed by varying these two thresholds, including the existence and dynamics of sliding mode, and the existence and global stability of equilibrium. It is shown that the model solutions ultimately converge to a pseudoequilibrium or a pseudoattractor on the switching surface, or a real equilibrium. The obtained results indicate that, by choosing susceptible and infected thresholds properly, the infection number can be remained below or at an acceptable level.

Modeling the COVID-19 epidemic in Bolivia

The first cases of COVID-19 appeared in Bolivia on March 10. Since then and until September 24,132,618 people have been infected, 7765 have died, and 92,101 have recovered; the virus has spread throughout the country, but the departments of Santa Cruz, La Paz, and Cochabamba account for the overwhelming percentage of infected, recovered and dead. We analyze the spread of the virus utilizing a SIR model. We find that a maximum fraction of infected individuals occurs on June 17, when around 28% of the population is infected; when the epidemic begins to subside, 54% of the population is in the recovered category, indicating that more than half of the population will have been infected by COVID-19 during some period of the epidemic. There is an uptick in the number of susceptible individuals after July 1, highlighting that the relaxing of mitigation measures might have happened too soon.

Control of malaria outbreak using a non‐linear robust strategy with adaptive gains

The aim of this study is to develop a non-linear robust controller with adaptive gains in order to prevent malaria epidemic as a positive system with an uncertain model. The malaria outbreak is modelled by seven non-linear coupled differential equations for the population variables: susceptible, exposed, symptomatic infected and recovered humans and the susceptible, exposed and infected mosquitoes. The non-linear robust adaptive integral-sliding-mode controller is developed in order to appropriately adjust the use of treated bednets, treatment rate of infected individuals and the use of insecticide spray to control malaria epidemic. Accordingly, the numbers of exposed and infected humans and infected mosquitoes are decreased to zero by employing the designed control scheme. However, the numbers of susceptible individuals and mosquitoes are increased due to their birth rates and loss of malaria immunity in recovered individuals. The Lyapunov stability theorem is used to prove the stability, robustness and tracking convergence of the closed-loop system in the presence of modelling uncertainties. The simulation results demonstrate that by increasing the therapy time interval, the use of treated bednets and insecticide spray is decreased; however, a higher treatment rate is required for the infected population.

A comparison of some control strategies for a non-integer order tuberculosis model

The aim of this paper is to investigate some optimal control strategies for a generalized tuberculosis model consisting of four compartments. We construct the model with the use of Caputo time fractional derivative. Contribution of distancing control, latent case finding control, case holding control and their combinations are discussed and the optimality system is obtained based on the Hamiltonian principle. Additionally, the non-negativity and boundedness of the solution are shown. We present some illustrative examples to determine the most effective strategy to minimize the number of infected people and maximize the number of susceptible individuals. Moreover, we discuss the contribution of the Caputo derivative and the order of the fractional derivative to efficiency of the control strategies.