Search

COVID-19 has become a serious pandemic affecting many countries around the world since it was discovered in 2019. In this research, we present a compartmental model in ordinary differential equations for COVID-19 with vaccination, inflow of infected and a generalized contact rate. Existence of a unique global positive solution of the model is proved, followed by stability analysis of the equilibrium points. A control problem is presented, with vaccination as well as reduction of the contact rate by way of education, law enforcement or lockdown. In the last section, we use numerical simulations with data applicable to South Africa, for supporting our theoretical results. The model and application illustrate the interesting manner in which a diseased population can be perturbed from within itself. [ABSTRACT FROM AUTHOR]

South Africa has the highest number of people living with the human immunodeficiency virus (HIV) in the world, accounting for nearly one in five people living with HIV globally. As of 2021, 8 million people in South Africa were infected with HIV, which is 13% of the country's total population. Approximately 450,000 people in the country develop tuberculosis (TB) disease every year, and 270,000 of those are HIV positive. This suggests that being HIV positive significantly increases one's susceptibility to TB, accelerating the spread of the epidemic. To better understand the disease burden at the population level, a Susceptible–Infected–Recovered–Dead (SIRD) TB–HIV co-infection epidemic model is presented. Parameter values are estimated using the method of moments. The disease-free equilibrium and basic reproduction number of the model are also obtained. Finally, numeric simulations are carried out for a 30-year period to give insights into the transmission dynamics of the co-infection. [ABSTRACT FROM AUTHOR]

African horse sickness is an equine orbivirus transmitted by Culicoides Latreille biting midges. In the last 80 years, it has caused several devastating outbreaks in the equine population in Europe, the Far and Middle East, North Africa, South-East Asia, and sub-Saharan Africa. The disease is endemic in South Africa; however, a unique control area has been set up in the Western Cape where increased surveillance and control measures have been put in place. A deterministic metapopulation model was developed to explore if an outbreak might occur, and how it might develop, if a latently infected horse was to be imported into the control area, by varying the geographical location and months of import. To do this, a previously published ordinary differential equation model was developed with a metapopulation approach and included a vaccinated horse population. Outbreak length, time to peak infection, number of infected horses at the peak, number of horses overall affected (recovered or dead), re-emergence, and Rv (the basic reproduction number in the presence of vaccination) were recorded and displayed using GIS mapping. The model predictions were compared to previous outbreak data to ensure validity. The warmer months (November to March) had longer outbreaks than the colder months (May to September), took more time to reach the peak, and had a greater total outbreak size with more horses infected at the peak. Rv appeared to be a poor predictor of outbreak dynamics for this simulation. A sensitivity analysis indicated that control measures such as vaccination and vector control are potentially effective to manage the spread of an outbreak, and shortening the vaccination window to July to September may reduce the risk of vaccine-associated outbreaks. Author summary: African Horse Sickness is a devastating global equine disease which results in high numbers of deaths. In South Africa it is considered endemic, and this poses implications for trade and exportation of horses out of the country. As a result, South Africa has developed a "control area" where there are increased surveillance and control strategies to keep it free from African horse sickness. Our research explores where and how an outbreak may occur in the "control area" if a horse harbouring the virus were to be imported into the region. We developed a mathematical simulation which considered the differences in horse population numbers, midge population numbers, environmental temperature, and vaccination status of horses in different areas across the "control area". This helped to determine how many horses would be affected at the end of the outbreak as well as at the peak, how long the outbreak would occur, and the reproduction number (Rv), and how this varied across the study area. Our research uncovers insights into the African horse sickness outbreak dynamics of the "control area" and helps provide information to further develop control strategies. [ABSTRACT FROM AUTHOR]