摘要
<span style="font-family:Verdana;">For Madagascar, with the uncertainty over vaccines against the novel coronavirus 2019 and its variants, non-pharmaceutical approach is widely used. Our objective is to propose a mathematical control model which will serve as a tool to help decision-makers in the strategy to be implemented to better face the pandemic</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">.</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> By separating asymptomatic cases which are often not reported and symptomatic who are hospitalized after tests;we develop a mathematical model of the propagation of covid-19 in Madagascar, by integrating control strategies. We study the stability of the model by expressing the basic reproduction number using the next-generation matrix. Simulation with different parameters shows the effects of non-pharmaceutical measures on the speed of the disease spread. By integrating a control parameter linked to compliance with barrier measures in the virus propagation equation, we were able to show the impacts of the implementation of social distancing measures on the basic reproduction number. The strict application of social distancing measures and total confinement </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> unfavorable for economic situation even if they allow the contamination to be reduced quickly. Without any restrictions, the disease spreads at high speed and the peak is reached fairly quickly. In this condition, hospitals are overwhelmed and the death rate increases rapidly. With 50% respect for non-pharmaceutical strategies such as rapid detection and isolation of positive cases and barrier gestures;the basic reproduction numbe
<span style="font-family:Verdana;">For Madagascar, with the uncertainty over vaccines against the novel coronavirus 2019 and its variants, non-pharmaceutical approach is widely used. Our objective is to propose a mathematical control model which will serve as a tool to help decision-makers in the strategy to be implemented to better face the pandemic</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">.</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> By separating asymptomatic cases which are often not reported and symptomatic who are hospitalized after tests;we develop a mathematical model of the propagation of covid-19 in Madagascar, by integrating control strategies. We study the stability of the model by expressing the basic reproduction number using the next-generation matrix. Simulation with different parameters shows the effects of non-pharmaceutical measures on the speed of the disease spread. By integrating a control parameter linked to compliance with barrier measures in the virus propagation equation, we were able to show the impacts of the implementation of social distancing measures on the basic reproduction number. The strict application of social distancing measures and total confinement </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> unfavorable for economic situation even if they allow the contamination to be reduced quickly. Without any restrictions, the disease spreads at high speed and the peak is reached fairly quickly. In this condition, hospitals are overwhelmed and the death rate increases rapidly. With 50% respect for non-pharmaceutical strategies such as rapid detection and isolation of positive cases and barrier gestures;the basic reproduction numbe
