Predator-Prey Model with Prey Harvesting, Holling Response Function of Type III and SIS Disease

The populations of prey and predator interact with prey harvesting. When there is no predator, the logistic equation models the behavior of the preys. For interactions between preys and predators, we use the generalized Holling response function of type III. This function which models the consumption of preys by predators is such that the predation rate of predators increases when the preys are few and decreases when they reach their satiety. Our main goal is to analyze the influence of a SIS infectious disease in the community. The epidemiological SIS model with simple mass incidence is chosen, where only susceptibles and infectious are counted. We assume firstly that the disease spreads only among the prey population and secondly that it spreads only among the predator population. There are many bifurcations as: Hopf bifurcation, transcritical bifurcation and saddle-node bifurcation. The results indicate that either the disease dies out or persists and then, at least one population can disappear because of infection. For some particular choices of the parameters however, there exists endemic equilibria in which both populations survive. Numerical simulations on MATLAB and SCILAB are used to illustrate our results

Optimal control using state-dependent Riccati equation of lost of sight in a tuberculosis model

International audienc

Analysis of an Age-structured SIL model with demographics process and vertical transmission

We consider a mathematical SIL model for the spread of a directly transmitted infectious disease in an age-structured population; taking into account the demographic process and the vertical transmission of the disease. First we establish the mathematical well-posedness of the time evolution problem by using the semigroup approach. Next we prove that the basic reproduction ratio R0 is given as the spectral radius of a positive operator, and an endemic state exist if and only if the basic reproduction ratio R0 is greater than unity, while the disease-free equilibrium is locally asymptotically stable if R0<1. We also show that the endemic steady states are forwardly bifurcated from the disease-free steady state when R0 cross the unity. Finally we examine the conditions for the local stability of the endemic steady states

Analysis of an Age-structured SIL model with demographics process and vertical transmission

International audienceWe consider a mathematical SIL model for the spread of a directly transmitted infectious disease in an age-structured population; taking into account the demographic process and the vertical transmission of the disease. First we establish the mathematical well-posedness of the time evolution problem by using the semigroup approach. Next we prove that the basic reproduction ratio R0 is given as the spectral radius of a positive operator, and an endemic state exist if and only if the basic reproduction ratio R0 is greater than unity, while the disease-free equilibrium is locally asymptotically stable if R0<1. We also show that the endemic steady states are forwardly bifurcated from the disease-free steady state when R0 cross the unity. Finally we examine the conditions for the local stability of the endemic steady states

Development and analysis of a malaria transmission mathematical model with seasonal mosquito life‐history traits

Please read abstract in the article.http://wileyonlinelibrary.com/journal/sapm2021-05-01hj2020Geography, Geoinformatics and Meteorolog

Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic

ABSTRACT: In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing. AUTHOR SUMMARY: COVID-19 infected individuals differ in the way they spread the infection depending on their age or on the number of days elapsed since the contamination. This individual heterogeneity can impact the design of public health control measures to contain epidemics. Using optimal control theory, we identify a strategy that minimizes deaths and costs due to the implementation of the control measures themselves. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). This strategy consists in rapidly intervening in older populations to protect the older people during the initial phase of the epidemic and (if the cost is intermediate or low) to control the epidemic, before progressively alleviating this control. Interventions in the younger population can occur later if the cost associated with the intervention is low. Such interventions targeted at younger people aim at suppressing the epidemic

Investigating the resurgence of malaria prevalence in South Africa between 2015 and 2018 : a scoping review

BACKGROUND : Malaria remains a serious concern in most African countries, causing nearly one million deaths globally every year. This review aims to examine the extent and nature of the resurgence of malaria transmission in South Africa. METHODS : Using the Arksey and O'Malley framework, this scoping review includes articles published between the years 2015 and 2018 on the resurgence of malaria occurrence in South Africa. Articles were searched between October 2018 to January 2019 using the following electronic databases: CINAHL, Pubmed, Science Direct and SCOPUS. Grey literature from Google Scholar was also hand searched. Key search terms and subject headings such as climate variables, climate changes, climatic factors, malaria resurgence, malaria reoccurrence and malaria increase over epidemic regions in South Africa were used to identify relevant articles. Three independent reviewers performed the selection and characterization of articles, and the data collected were synthesized qualitatively. RESULTS : A total number of 534 studies were identified. Among these, 24 studies met the inclusion criteria. The results were grouped by factors (four main themes) that influenced the malaria resurgence: Climatic, Epidemiological, Socio-economic, and Environmental factors. Climatic factors were found to be the major factor responsible for the resurgence of malaria, as more than 55% of the selected articles were climate-focused. This was followed by epidemiological, socio-economic and environmental factors, in that order. Grey literature from Google Scholar yielded no results. CONCLUSION : This study shows that malaria transmission in South Africa is more associated with climate. Climate-based malaria models could be used as early warning systems for malaria over the epidemic regions in South Africa. Since epidemiological factors also play significant roles in malaria transmission, regular and unrelaxed use of Indoor Residual Spraying (IRS) should be encouraged in these regions. Individuals should also be educated on the importance and the usefulness of these deliveries. While some studies have indicated that the vectors have developed resistance to insecticides, continuous research on developing new insecticides that could alter the resistance are encouraged. Furthermore, all efforts to eradicate malaria in South Africa must also target malaria-endemic neighbouring countries.The University of Pretoria Institute for Sustainable Malaria Control (UP ISMC) and Malaria Research Control (MRC)https://benthamopen.com/TOPHJ/home/am2021School of Health Systems and Public Health (SHSPH