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Approximately one-third of the world's population that is at risk to malaria lives in India. Plasmodium falciparum, a deadly form of malaria, accounts for about 50% of the cases there. Since 1940s, India has used a number of programs to combat the disease with variable success. Since 1998, the total numbers of malaria cases, and in particular P. falciparum cases, have been steadily declining, making India one of the success stories among the countries supported by the Roll Back Malaria (RBM) Partnership. This article considers India's P. falciparum control methods from the perspective of a Ross-MacDonald type model. The model is fitted to the P. falciparum cases in India over the period 1983–2009. We focus on the disease reproduction number as being a measure of success of programs. Before the start of RBM measures, the disease reproduction number was , meaning that the incidence of disease was increasing among the population. With the new control measures , suggesting that P.falciparum cases may be declining to zero but extremely slowly. The model here projects 0.734 million cases of P. falciparum malaria for 2010, down from 1.14 million cases in 2000. This impressive 36% decrease falls somewhat short of the RBM's goal of 50% reduction. However, a sensitivity analysis of the disease reproduction number done here suggests that India's control programs do apply controls at the most critical points in the disease cycle; namely, mosquito biting rates, mosquito mortality, and treatment of infected humans. This suggests that as more resources become available, they should be applied to strengthen these controls. The novelty here is in fitting recent data on malaria from India to derive current values of the disease reproduction number.

At present, H5N1 avian influenza (AI) is a zoonotic disease where the transmission to humans occurs from infected domestic birds. Since 2003, more than 500 people have been infected and nearly 60% of them have died. If the H5N1 virus becomes efficiently human-to-human transmittable, a pandemic will occur with potentially high mortality. A mathematical model of AI, which involves human influenza, is introduced to better understand the complex epidemiology of AI and the emergence of a pandemic strain. Demographic and epidemiological data on birds and humans are used for the parameterization of the model. The differential equation system faithfully projects the cumulative number of H5N1 human cases and captures the dynamics of the yearly cases. The model is used to rank the efficacy of the current control measures used to prevent the emergence of a pandemic strain. We find that culling without re-population and vaccination are the two most efficient control measures each giving 22% decrease in the number of H5N1 infected humans for each 1% change in the affected parameters (μ_b, ν_b for culling and β_b, ν_b for vaccination). Control measures applied to humans, such as wearing protective gear, are not very efficient, giving less than 1% decrease in the number of H5N1 infected humans for each 1% decrease in β_Y, the bird-to-human transmission coefficient of H5N1. Furthermore, we find that should a pandemic strain emerge, it will invade, possibly displacing the human influenza virus in circulation at that time. Moreover, higher prevalence levels of human influenza will obstruct the invasion capabilities of the pandemic H5N1 strain. This effect is not very pronounced, as we find that 1% increase in human influenza prevalence will decrease the invasion capabilities of the pandemic strain with 0.006%.

The avian influenza A (H7N9) virus is one subtype of influenza viruses, which has previously been isolated only in birds. Recently, an outbreak of a new avian influenza (H7N9) in China has resulted in numerous infections and high mortality in the humans. The H7N9 virus is low pathogenic in poultry and high pathogenic in human and that is critically different from other avian influenza viruses. An increasing number of the new H7N9 cases and the high mortality have caused a serious global concern. Here, based on the reported data, we propose and analyze an SE-SEIS avian–human influenza model. We prove the global stability results for both the disease-free equilibrium point and the endemic equilibrium point by using a general Bendixson–Dulac theorem. Our reported theoretical results of this paper are expected to help in exploring the development of efficient methods to controlling the spread of avian influenza A(H7N9).

In this paper, we have formulated a compartmental epidemic model with exponentially decaying transmission rates to understand the Ebola transmission dynamics and study the impact of control measures to basic public health. The epidemic model exhibits two equilibria, namely, the disease-free and unique endemic equilibria. We have calculated the basic reproduction number through next generation matrix and investigated the spatial spread of the epidemic via reaction–diffusion modeling. Instead of fitting the model to the observed pattern of spread, we have used previously estimated parameter values and examined the efficacy of predictions of the designed model vis-à-vis the pattern of spread observed in Sierra Leone, West Africa. Further, we conducted a sensitivity analysis to determine the extent to which improvement in predictions is achievable through better parameterization.

We performed numerical simulations with and without control measure for the designed model system. A significant reduction in infection and death cases were observed when proper control measures are incorporated in the model system. Two-dimensional simulation experiments show that infectious population and the number of deaths will increase up to one and a half years without control, but it will decline after two years. We have reported the numerical results, and it closely matches with the real situation in Sierra Leone.

In December 2019, a novel coronavirus, SARS-COV-2, was identified among patients in Wuhan, China. Two strict control measures, i.e., putting Wuhan on lockdown and taking strict quarantine rule, were carried out to contain the spread of COVID-19. Based on the different control measures, we divided the transmission process of COVID-19 into three stages. An SEIHR model was established to describe the transmission dynamics and was applied to fit the published data on the confirmed cases of Wuhan city from December 31, 2019 to March 25, 2020 to deduce the time when the first patient with COVID-19 appeared. The basic reproduction number was estimated in the first stage to demonstrate the number of secondary infectious cases generated by an average infectious case in the absence of policy intervention. The effective reproduction numbers in second and third stages were estimated to evaluate the effects of the two strict control measures. In addition, sensitivity analysis of the reproduction number according to model parameters was executed to demonstrate the effect of the control measures for containing the spread of COVID-19. Finally, the numerical calculation method was applied to investigate the influence of the different control measures on the spread of COVID-19. The results indicated that following the strict quarantine rule was very effective, and reducing the effective contact rates and improving the diagnosis rate were crucial in reducing the effective reproduction number, and taking control measures as soon as possible can effectively contain a larger outbreak of COVID-19. But a bigger challenge for us to contain the spread of COVID-19 was the transmission from the asymptomatic carriers, which required to raising the public awareness of self-protection and keeping a good physical protection.

Control Measures for Severe Acute Respiratory Syndrome (SARS) in Taiwan.

Beijing Formulates Contingency Plan to Guard Against SARS Resurgence.

The re-emergence of the Ebola virus disease has pushed researchers to investigate more on this highly deadly disease in order to better understand and control the outbreak and recurrence of epidemics. It is in this perspective that we formulate a realistic mathematical model for the dynamic transmission of Ebola virus disease, incorporating relevant control measures and factors such as ban on eating bush-meat, social distancing, observance of hygiene rules and containment, waning of the vaccine-induced, imperfect contact tracing and vaccine efficacy, quarantine, hospitalization and screening to fight against the spread of the disease. First, by considering the constant control parameters case, we thoroughly compute the control reproduction number ${{ℛ}}_0^c$ from which the dynamics of the model is analyzed. The existence and stability of steady states are established under appropriate assumptions on ${{ℛ}}_0^c$. Also, the effect of all the control measures is investigated and the global sensitivity analysis of the control reproduction number is performed in order to determine the impact of parameters and their relative importance to disease transmission and prevalence. Second, in the time-dependent control parameters case, an optimal control problem is formulated to design optimal control strategies for eradicating the disease transmission. Using Pontryagin’s Maximum Principle, we derive necessary conditions for optimal control of the disease. The cost-effectiveness analysis of all combinations of the control measures is made by calculating the infection averted ratio and the incremental cost-effectiveness ratio. This reveals that combining the four restrictive measures conveyed through educational campaigns, screening, safe burial and the care of patients in health centers for better isolation is the most cost-effective among the strategies considered. Numerical simulations are performed to illustrate the theoretical results obtained.

In this chapter, a brief introduction is presented to radioactive pollution and its management. Both natural and artificial sources of radiation are discussed with special attention to the relative importance of each source. In addition, radioactive isotope applications in tracing, radiography, insect control, food preservation, medical diagnoses, therapy, sterilization, and power generation are briefly described. Sources of radioactive pollution are identified including nuclear weapon tests, nuclear accidents, routine effluent release into the environment, and radioactive waste. Radioactive pollution prevention measures are presented including: treaties, regulations and standards, and technical methods to control pollution. The risk-informed regulatory process is briefly described, along with the technical methods to control radioactive wastes via site selection criteria, design of radioactive waste disposal facilities, and performance assessment.