A COVID-19 mathematical model of at-risk populations with non-pharmaceutical preventive measures: The case of Brazil and South Africa.

This work examines a mathematical model of COVID-19 among two subgroups: low-risk and high-risk populations with two preventive measures; non-pharmaceutical interventions including wearing masks, maintaining social distance, and washing hands regularly by the low-risk group. In addition to the interventions mentioned above, high-risk individuals must take extra precaution measures, including telework, avoiding social gathering or public places, etc. to reduce the transmission. Those with underlying chronic diseases and the elderly (ages 60 and above) were classified as high-risk individuals and the rest as low-risk individuals. The parameter values used in this study were estimated using the available data from the Johns Hopkins University on COVID-19 for Brazil and South Africa. We evaluated the effective reproduction number for the two countries and observed how the various parameters affected the effective reproduction number. We also performed numerical simulations and analysis of the model. Susceptible and infectious populations for both low-risk and high-risk individuals were studied in detail. Results were displayed in both graphical and table forms to show the dynamics of each country being studied. We observed that non-pharmaceutical interventions by high-risk individuals significantly reduce infections among only high-risk individuals. In contrast, non-pharmaceutical interventions by low-risk individuals have a significant reduction in infections in both subgroups. Therefore, low-risk individuals' preventive actions have a considerable effect on reducing infections, even among high-risk individuals.

Impact of Public Health Education Program on the Novel Coronavirus Outbreak in the United States.

The coronavirus outbreak in the United States continues to pose a serious threat to human lives. Public health measures to slow down the spread of the virus involve using a face mask, social-distancing, and frequent hand washing. Since the beginning of the pandemic, there has been a global campaign on the use of non-pharmaceutical interventions (NPIs) to curtail the spread of the virus. However, the number of cases, mortality, and hospitalization continue to rise globally, including in the United States. We developed a mathematical model to assess the impact of a public health education program on the coronavirus outbreak in the United States. Our simulation showed the prospect of an effective public health education program in reducing both the cumulative and daily mortality of the novel coronavirus. Finally, our result suggests the need to obey public health measures as loss of willingness would increase the cumulative and daily mortality in the United States.

COVID-19 intervention models: An initial aggressive treatment strategy for controlling the infection.

The novel coronavirus (COVID-19) outbreak emerged in December 2019. The disease has caused loss of many lives and has become an unprecedented threat to public health worldwide. We develop simple COVID-19 epidemic models to study treatment strategies to control the pandemic. The results show that eradication of the disease is possible if the efficacy of treatment is perfect. We also investigate the existence of a dual-rate effect. Conditions under which the effect occurs are derived. When the effect is present, a tactic to control the infection might be to initially treat infected individuals aggressively at a relatively high rate to drive the prevalence to a lower region that can be maintained in the long run at relatively moderate rate and cost.

A fractional order approach to modeling and simulations of the novel COVID-19.

The novel coronavirus (SARS-CoV-2), or COVID-19, has emerged and spread at fast speed globally; the disease has become an unprecedented threat to public health worldwide. It is one of the greatest public health challenges in modern times, with no proven cure or vaccine. In this paper, our focus is on a fractional order approach to modeling and simulations of the novel COVID-19. We introduce a fractional type susceptible-exposed-infected-recovered (SEIR) model to gain insight into the ongoing pandemic. Our proposed model incorporates transmission rate, testing rates, and transition rate (from asymptomatic to symptomatic population groups) for a holistic study of the coronavirus disease. The impacts of these parameters on the dynamics of the solution profiles for the disease are simulated and discussed in detail. Furthermore, across all the different parameters, the effects of the fractional order derivative are also simulated and discussed in detail. Various simulations carried out enable us gain deep insights into the dynamics of the spread of COVID-19. The simulation results confirm that fractional calculus is an appropriate tool in modeling the spread of a complex infectious disease such as the novel COVID-19. In the absence of vaccine and treatment, our analysis strongly supports the significance reduction in the transmission rate as a valuable strategy to curb the spread of the virus. Our results suggest that tracing and moving testing up has an important benefit. It reduces the number of infected individuals in the general public and thereby reduces the spread of the pandemic. Once the infected individuals are identified and isolated, the interaction between susceptible and infected individuals diminishes and transmission reduces. Furthermore, aggressive testing is also highly recommended.

The impact of implementing HIV prevention policies therapy and control strategy among HIV and AIDS incidence cases in Malaysia.

Malaysia is faced with a high HIV/AIDS burden that poses a public health threat. We constructed and applied a compartmental model to understand the spread and control of HIV/AIDS in Malaysia. A simple model for HIV and AIDS disease that incorporates condom and uncontaminated needle-syringes interventions and addresses the relative impact of given treatment therapy for infected HIV newborns on reducing HIV and AIDS incidence is presented. We demonstrated how treatment therapy for new-born babies and the use of condoms or uncontaminated needle-syringes impact the dynamics of HIV in Malaysia. The model was calibrated to HIV and AIDS incidence data from Malaysia from 1986 to 2011. The epidemiological parameters are estimated using Bayesian inference via Markov chain Monte Carlo simulation method. The reproduction number optimal for control of the HIV/AIDS disease obtained suggests that the disease-free equilibrium was unstable during the 25 years. However, the results indicated that the use of condoms and uncontaminated needle-syringes are pivotal intervention control strategies; a comprehensive adoption of the intervention may help stop the spread of HIV disease. Treatment therapy for newborn babies is also of high value; it reduces the epidemic peak. The combined effect of condom use or uncontaminated needle-syringe is more pronounced in controlling the spread of HIV/AIDS.

A model of insect control with imperfect treatment.

Insecticide spraying of housing units is an important control measure for vector-borne infections such as Chagas disease. However, some vectors may survive treatment, due to imperfect spraying by the operator or because they hide deep in the cracks or other places, and re-emerge in the same unit when the effect of the insecticide wears off. While several mathematical models of this phenomenon have been previously described and studied in the literature, the model presented here is more basic than existing ones. Thus it is more amenable to mathematical analysis, which is carried out here. In particular, we demonstrate that an initially very high spraying rate may push the system into a region of the state space with low endemic levels of infestation that can be maintained in the long run at relatively moderate cost, while in the absence of an aggressive initial intervention the same average cost would only allow a much less significant reduction in long-term infestation levels.

Models of Disease Vector Control: When Can Aggressive Initial Intervention Lower Long-Term Cost?

Insecticide spraying of housing units is an important control measure for vector-borne infections such as Chagas disease. As vectors may invade both from other infested houses and sylvatic areas and as the effectiveness of insecticide wears off over time, the dynamics of (re)infestations can be approximated by [Formula: see text]-type models with a reservoir, where housing units are treated as hosts, and insecticide spraying corresponds to removal of hosts. Here, we investigate three ODE-based models of this type. We describe a dual-rate effect where an initially very high spraying rate can push the system into a region of the state space with low endemic levels of infestation that can be maintained in the long run at relatively moderate cost, while in the absence of an aggressive initial intervention the same average cost would only allow a much less significant reduction in long-term infestation levels. We determine some sufficient and some necessary conditions under which this effect occurs and show that it is robust in models that incorporate some heterogeneity in the relevant properties of housing units.