Geodesic
SIARD model and effect of lockdown on the dynamics of COVID-19 disease with non total immunity
M.A. Aziz-Alaoui1, 2, 3 ; F. Najm4 ; R. Yafia4
1 Normandie Univ, 76600 Le Havre, France.
2 ULH, LMAH, 76600 Le Havre. France
3 FR-CNRS-3335, ISCN, 25 rue Ph. Lebon, 76600 Le Havre, France.
4 Laboratory of Analysis, Geometry and Applications (LAGA), Department of Mathematics Faculty of Sciences, Ibn Tofail University, Campus Universitaire BP 133, Kenitra, Morocco.
Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 31 Cet article a éte moissonné depuis la source EDP Sciences

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We propose a new compartmental mathematical model describing the transmission and the spreading of COVID-19 epidemic with a special focus on the non-total immunity. The model (called SIARD) is given by a system of differential equations which model the interactions between five populations “susceptible”, “reported infectious”, “unreported infectious”, “recovered with/without non total immunity” and “death”. Depending on the basic reproduction number, we prove that the total immunity induces local stability-instability of equilibria and the epidemic may disappear after a first epidemic wave and more epidemic waves may appear in the case of non-total immunity. Using the sensitivity analysis we identify the most sensitive parameters. Numerical simulations are carried out to illustrate our theoretical results. As an application, we found that our model fits well the Moroccan epidemic wave, and predicts more than one wave for French case.
DOI : 10.1051/mmnp/2021025

M.A. Aziz-Alaoui 1, 2, 3 ; F. Najm 4 ; R. Yafia 4

1 Normandie Univ, 76600 Le Havre, France.
2 ULH, LMAH, 76600 Le Havre. France
3 FR-CNRS-3335, ISCN, 25 rue Ph. Lebon, 76600 Le Havre, France.
4 Laboratory of Analysis, Geometry and Applications (LAGA), Department of Mathematics Faculty of Sciences, Ibn Tofail University, Campus Universitaire BP 133, Kenitra, Morocco. 
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     title = {SIARD model and effect of lockdown on the dynamics of {COVID-19} disease with non total immunity},
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M.A. Aziz-Alaoui; F. Najm; R. Yafia. SIARD model and effect of lockdown on the dynamics of COVID-19 disease with non total immunity. Mathematical modelling of natural phenomena, Tome 16 (2021), article  no. 31. doi: 10.1051/mmnp/2021025

[1] R.M. Anderson and R.M. May, Infectious Diseases of Humans. Oxford University Press (1991).

[2] F. Brauer and C. Castillo-Chavezv, Mathematical Models in Population Biology and Epidemiology. Springer (2001).

[3] De Chang Time kinetics of viral clearance and resolution of symptoms in novel coronavirus infection Am. J. Respirat. Critical Care Med 2020 1150 1152

[4] O. Diekmann and J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley (2000).

[5] O. Diekmann, J.A.P. Heesterbeek, J.A.J. Metz On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations J. Math. Biol 1990 365 382

[6] O. Diekmann and J.A.P. Heesterbeek, Mathematical epidemiology of infectious diseases : model building, analysis and interpretation. Wiley (2000).

[7] V. Gupta, R.C. Bhoyar, A. Jain, S. Srivastava, R. Upadhayay, M. Imran Asymptomatic reinfection in two healthcare workers from India with genetically distinct SARS-CoV-2 2020

[8] W.O. Kermack, A.G. Mckendrick A contribution to the mathematical theory of epidemics Proc. Roy. Soc. A: Math. Phys. Eng. Sci 1927 700 721

[9] L. Lan, D. Xu, G. Ye Positive RT-PCR test results in patients recovered from COVID-19 JAMA 2020 1502 1503

[10] F.N. Ngoteya, Y.N. Gyekye Sensitivity analysis of parameters in a competition model Appl. Comput. Math 2015 363 368

[11] I. Petersen, A. Phillips Three quarters of people with SARS-CoV-2 infection are asymptomatic: analysis of English household survey data Clin. Epidemiol 2020 1039 1043

[12] B. Prado-Vivar, M. Becerra-Wong, J.J. Guadalupe, S. Marquez, B. Gutierrez, P. Rojas-Silva COVID-19 ReInfection by a Phylogenetically Distinct SARS-CoV-2 Variant, First Confirmed Event in South America SSRN 2020

[13] F.A. Rihan, H.J. Alsakaji, C. Rajivganthi Stochastic SIRC epidemic model with time-delay for COVID-19 Adv Differ Equ 2020 502

[14] F.A. Rihan, H.J. Alsakaji Persistence and extinction for stochastic delay differential model of prey predator system with hunting cooperation in predators Adv. Differ. Equ 2020 124

[15] R. Tillett Genomic evidence for a case of reinfection with SARS-CoV-2 SSRN Electr. J 2020 1 7

[16] K.K.-W. To, I.F.-N. Hung, J.D. Ip, A.W.-H. Chu, W.-M. Chan, A.R. Tam COVID-19 re-infection by a phylogenetically distinct SARS-coronavirus-2 strain confirmed by whole genome sequencing Clin. Infectious Dis 2020

[17] J. Van Elslande, P. Vermeersch, K. Vandervoort, T. Wawina-Bokalanga, B. Vanmechelen, E. Wollants Symptomatic SARS-CoV-2 reinfection by a phylogenetically distinct strain Clin. Infectious Dis 2020

[18] P. Van Den Driessche, J. Watmough Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission Math. Biosci 2002 29 48

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