Mathematical Model and Non-Pharmaceutical Control of the Coronavirus 2019 Disease in Madagascar

Abstract

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. 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 is 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 number R 0 can go down from 3 to 1.7. The pressures on the economic and social situation are rather viable. It is the most suitable for the Malagasy health system. The results proposed are a way to control the spread of the disease and limit its devastation in a country like Madagascar.

Cross-sectional cycle threshold values reflect epidemic dynamics of COVID-19 in Madagascar

“…Estimation of R t , or its related counterpart, r, the epidemic growth rate ( Wallinga and Lipsitch, 2007 , Park et al, 2020 ), from available case count data is challenged by limitations or variability in surveillance, uncertainty surrounding the shape of disease parameter distributions, and delays in reporting ( Gostic et al, 2020 ). Despite the enormity of these challenges in the limited surveillance settings common to many lower- and middle-income countries (LMICs), real-time estimation of R t from COVID-19 case-counts has been attempted for most regions of the globe ( $author1$ et al, 7]</id><AuthGrp><Author><in>S.</in><dl> </dl><au>Abbott</au></Author><dl>, </dl><Author><in>J.</in><dl> </dl><au>Hellewell</au></Author><dl>, </dl><Author><in>R.N.</in><dl> </dl><au>Thompson</au></Author><dl>, </dl><Author><in>K.</in><dl> </dl><au>Sherratt</au></Author><dl>, </dl><Author><in>H.P.</in><dl> </dl><au>Gibbs</au></Author><dl>, </dl><Author><in>N.I.</in><dl> </dl><au>Bosse</au></Author><dl>, </dl><Author><in>J.D.</in><dl> </dl><au>Munday</au></Author><dl>, </dl><Author><in>S.</in><dl> </dl><au>Meakin</au></Author><dl>, </dl><Author><in>E.L.</in><dl> </dl><au>Doughty</au></Author><dl>, </dl><Author><in>J.Y.</in><dl> </dl><au>Chun</au></Author><dl>, </dl><Author><in>Y.-W.D.</in><dl> </dl><au>Chan</au></Author><dl>, </dl><Author><in>F.</in><dl> </dl><au>Finger</au></Author><dl>, </dl><Author><in>P.</in><dl> </dl><au>Campbell</au></Author><dl>, </dl><Author><in>A.</in><dl> </dl><au>Endo</au></Author><dl>, </dl><Author><in>C.A.B.</in><dl> </dl><au>Pearson</au></Author><dl>, </dl><Author><in>A.</in><dl> </dl><au>Gimma</au></Author><dl>, </dl><Author><in>T.</in><dl> </dl><au>Russell</au></Author><dl>, </dl><Author><in>C.C.</in><dl> </dl><au>modelling Group</au></Author><dl>, </dl><Author><in>S.</in><dl> </dl><au>Flasche</au></Author><dl>, </dl><Author><in>A.J.</in><dl> </dl><au>Kucharski</au></Author><dl>, </dl><Author><in>R.M.</in><dl> </dl><au>Eggo</au></Author><dl>, </dl><Author><in>S.</in><dl> </dl><au>Funk</au></Author></AuthGrp> ) and has been implemented locally in Madagascar ( Rasambainarivo et al, 2020 , Raherinirina et al, 2021 , Raherinirina et al, 2021 , Narison and Maltezos, 2021 ).…”