On the role of governmental action and individual reaction on COVID-19 dynamics in South Africa: A mathematical modelling study.

Mathematical models proffer a rational basis to epidemiologists and policy makers on how, where and when to control an infectious disease. Through mathematical models one can explore and provide solutions to phenomena which are difficult to measure in the field. In this paper, a mathematical model has been used to explore the role of government and individuals reaction to the recent outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The proposed framework incorporates all the relevant biological factors as well as the effects of individual behavioral reaction and government action such as travel restrictions, social distancing, hospitalization, quarantine and hygiene measures. Understanding the dynamics of this highly contagious SARS-CoV-2, which at present does not have any therapy assist the policy makers on evaluating the effectiveness of the control measures currently being implemented. Moreover, policy makers can have insights on short-and-long term dynamics of the disease. The proposed conceptual framework was combined with data on cases of coronavirus disease (COVID-19) in South Africa, March 2020 to early May 2020. Overall, our work demonstrated optimal conditions necessary for the infection to die out as well as persist.

Modelling cholera transmission dynamics in the presence of limited resources.

OBJECTIVES: We study the transmission dynamics of cholera in the presence of limited resources, a common feature of the developing world. The model is used to gain insight into the impact of available resources of the health care system on the spread and control of the disease. A deterministic model that includes a nonlinear recovery rate is formulated and rigorously analyzed. Limited treatment is described by inclusion of a special treatment function. Center manifold theory is used to show that the model exhibits the phenomenon of backward bifurcation. Matlab has been used to carry out numerical simulations to support theoretical findings. RESULTS: The model analysis shows that the disease free steady state is locally stable when the threshold [Formula: see text]. It is also shown that the model has multiple equilibria and the model exhibits the phenomenon of backward bifurcation whose implications to cholera infection are discussed. The results are useful for the public health planning in resource allocation for the control of cholera transmission.

Role of imitation and limited rehabilitation capacity on the spread of drug abuse.

OBJECTIVES: We formulate a mathematical model for the spread of drug abuse using non linear ordinary differential equations. The model seeks to investigate both peer influence and limited rehabilitation effects on the dynamics of drug abuse. Peer-influence is modelled through the mechanism of imitation and limited rehabilitation is described using a special treatment function. Center manifold theory is used to show that the model exhibits the phenomenon of backward bifurcation. Matlab has been used to carry out numerical simulations to support theoretical findings. RESULTS: The model analysis shows that the model has multiple equilibria. It has been shown that the classical [Formula: see text]-threshold is not the key to control drug abuse within a population. In fact drug abuse problems may persist in the population even with subthreshold values of [Formula: see text]. This was shown to result, in particular when, [Formula: see text], [Formula: see text] and [Formula: see text] are high enough such that [Formula: see text], [Formula: see text] and [Formula: see text]. The results suggest the need for comprehensive and accessible substance abuse treatment services to curtail drug abuse.