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.

In this paper, we present the impact of migration on the spread of HIV and AIDS cases. A simple model for HIV and AIDS that incorporates migration and addresses its contributions to the spread of HIV and AIDS cases was constructed. The model was calibrated to HIV and AIDS incidence data from Malaysia. We explore the use of Markov chain Monte Carlo (MCMC) simulation method to estimate uncertainty in all the unknown parameters incorporated in our proposed model. Among the migrant population, 1.5572e-01 were susceptible to HIV transmission, which constituted 67,801 migrants. A proportion of migrants, 6.3773e-04, were estimated to be HIV infected, constituting 278 migrants. There were 72 (per 10,000) migrants estimated to have had AIDS, representing a proportion of 1.6611e-08. The result suggests that the disease-free steady state was unstable since the estimated basic reproduction number $R_0$ was 2.0906 and 2.3322 for the models without and with migration, respectively. This is not a good indicator from the public health point of view, as the aim is to stabilize the epidemic at the disease-free equilibrium. The advantage of introduction of migration to the simple model validated the true $R_0$ and the transmission rate $\beta$ associated with HIV and AIDS epidemic disease in Malaysia. It also indicates an approximately 12 percentage points increase in the rate of HIV infection with migration.

Black pod disease is caused by fungi of the species Phytophthora palmivora or Phytophthora megakarya. The disease causes darkening of affected areas of cocoa trees and/or fruits and leads to significant reduction in crop yields and decreases lifespan of the plant. This study presents a simple S_1S_2IT-type model with variable population size to assess the impact of fungicide treatment on the dynamics of the black pod disease. We do both theoretical studies and numerical simulations of the model. In particular, we analyze the existence of equilibrium points and their stability, simulate the model using data on reported black pod cases from Ghana. In addition, we perform sensitivity analysis of the basic reproduction number with respect to the model parameters. The results show that the top three parameters that govern the dynamics of the black pod disease are the treatment rate, transmission rate, and planting rate of new trees

Since 2018, the EU commission has declared the Danish broiler industry to be Salmonella free. However, there is continuous Salmonella pressure from the environment, and a number of parent flocks and broiler flocks become infected annually. When a parent flock becomes infected, the infection can be transmitted vertically to the broiler flocks, before the parent flock is detected and destroyed, including the eggs at the hatchery. To address this issue, we developed stochastic dynamic modelling of transmission of Salmonella in parent flocks and combined that with the relation between flock prevalence and test sensitivity for environmental samples in the flock. Results suggested that after 10 and 100 infected hens were seeded, the likelihood of detecting an infected parent flock within the three first weeks after the infection was strongly influenced by the taking of five boot swabs (95% CI 70–100) instead of two (95% CI 40–100) or the supplementing of the two boot swabs by a dust sample (95% CI 43–100). Results suggest that the likelihood of detecting the broiler flock as infected in the program was estimated to at least 99% in broiler flock even if only one chicken was initially infected. These findings are of relevance for managing parent flocks and eggs at the hatchery in case of Salmonella infection in parent flocks in the Danish poultry.

Previous models of disease spread involving delay have used basic SIR (susceptible – infectious – recovery) formulae and approaches. This paper demonstrates how time-varying SEIRS (S – exposed – I – R – S) models can be extended with delay to produce wave propagations that simulate periodic wave fronts of disease spread in the context of population movements. The model also takes into account the natural mortality associated with the disease spread. Understanding the delay of an infectious disease is critical when attempting to predict where and how fast the disease will propagate. We use cellular automata to model the delay and its effect on the spread of infectious diseases where population movement occurs. We illustrate an approach using wavelet transform analysis to understand the impact of the delay on the spread of infectious diseases. The results indicate that including delay provides novel ways to understand the effects of migration and population movement on disease spread.

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.