key: cord-0825311-sjod3q3j authors: Xu, Peng title: Applying chemical reaction transition theory to predict the latent transmission dynamics of coronavirus outbreak in China date: 2020-02-25 journal: nan DOI: 10.1101/2020.02.22.20026815 sha: eeae21c913759e8cf4c345e561457fe7ef84480f doc_id: 825311 cord_uid: sjod3q3j The recent outbreak of the Covid-19 suggests a rather long latent phase that precludes public health officials to predict the pandemic transmission on time. Here we apply mass action laws and chemical transition theory to propose a kinetic model that accounts for viral transmission dynamics at the latent phase. This model is useful for authorities to make early preventions and control measurements that stop the spread of a deadly new virus. . CC-BY-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) The copyright holder for this preprint . https: //doi.org/10.1101 //doi.org/10. /2020 ' t r a n s m i s s i b l e ' a m o n g h u m a n s . P u b l i c h e a l t h a u t h o r i t i e s a n d e x p e r t f l e w t o W u h a n a n d a n n o u n c e d a f i r s t -g r a d e i n f e c t i o u s d i s e a s e a l a r m : m a j o r r a i l w a y s , a i r p o r t a n d b u s s t a t i o n s w e r e l o c k e d d o w n t o r e d u c e e v e r y p o s s i b l e c h a n c e o f v i r u s t r a n s m i s s i o n . T e n s o f h u n d r e d s o f p e o p l e w e r e s u s p e c t e d t o b e i n f e c t e d b y t h i s v i r u s a n d r e q u i r e h o s p i t a l i z a t i o n a n d s p e c i a l h e a l t h c a r e i n W u h a n . H o w e v e r , l a r g e p o p u l a t i o n s o f t h e l o c a l p a t i e n t c o u l d n o t b e h o s p i t a l i z e d d u e t o S t e p 7 d e s c r i b e s t h e d e c a y k i n e t i c s o f t h e a c t i v e v i r a l c a r r i e r t o a n i n a c t i v e v i r a l c a r r i e r . W i t h f u n d a m e n t a l m a s s a c t i o n l a w s , w e h a v e f o r m u l a t e d e i g h t d i f f e r e n t i a l e q u a t i o n s ( E q n . CC-BY-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10. 1101 /2020 References 1 . C h e n , N . , e t a l . , E p i d e m i o l o g i c a l a n d c l i n i c a l c h a r a c t e r i s t i c s o f 9 9 c a s e s o f 2 0 1 9 n o v e l c o r o n a v i r u s p n e u m o n i a i n W u h a n , C h i n a : a d e s c r i p t i v e s t u d y . T h e L a n c e t . 2 . . CC-BY-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) The copyright holder for this preprint S u p p l e m e n t a r y f i l e s ---------------------------------------------------------A p p e n d i x 1 : M a t l a b c o d e t o g e n e r a t e t h e e q u a t i o n s u s e d i n t h i s w o r k >> syms alpha k0 k1 k2 k3 k4 k5 k6 k7 n C_N(t) C_I(t) C_M(t) C_MS(t) C_S(t) C_SMS(t) C_R(t) C_D(t) C_Mtot C_Ntot >> eqn1 = diff(C_N,t) == alpha -k0*C_N; >> eqn2 = diff(C_S,t) == k0*C_N-k2*C_S*C_MS+k3*C_SMS; >> eqn3 = diff(C_I,t) == k4*C_SMS -k5*C_I-k6*C_I; >> eqn4 = diff(C_MS,t) == n*k1*C_I*C_M^n-k2*C_S*C_MS+(k3+k4)*C_SMS -k7*C_MS; >> eqn5 = diff(C_SMS,t) == k2*C_S*C_MS -(k3+k4)*C_SMS; >> eqn6 = diff(C_M,t) == k7*C_MS -n*k1*C_I*C_M^n; >> eqn7 = diff(C_R,t) == k5*C_I; >> eqn8 = diff(C_D,t) == k6*C_I; >> eqn9 = C_Mtot == C_MS +C_SMS+C_M; >> eqn10= C_Ntot == C_N + C_S + C_I + C_R + C_D +C_SMS; -------------------------------------------------------------------- . CC-BY-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10. 1101 /2020 function dydt = coronavirus10(t,y) dydt=zeros(8,1); k0=3.2;k1=1.2;k2=6.0;k3=0.06;k4=1.2;k5=0.09;k6=0.004;k7=20000; alpha=0.1; n=2.6; C_N = y(1); C_S = y(2); C_I = y(3); C_MS = y(4); C_SMS = y(5); C_M = y(6); C_R = y(7); C_D =y (8); dydt(1) = alpha -k0*C_N; dydt(2) = k0*C_N-k2*C_S*C_MS+k3*C_SMS; dydt(3) = k4*C_SMS -k5*C_I-k6*C_I; dydt(4) = n*k1*C_I*C_M^n-k2*C_S*C_MS+(k3+k4)*C_SMS -k7*C_MS; dydt(5) = k2*C_S*C_MS -(k3+k4)*C_SMS; dydt(6) = k7*C_MS -n*k1*C_I*C_M^n; dydt(7) = k5*C_I; dydt(8) = k6*C_I; end ------------------------------------------------------------------------------- ------------------------------------------------------------------------------A p p e n d i x 5 : M a t l a b c o d e t o g e n e r a t e F i g u r e 3 . . CC-BY-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10. 1101 /2020 >> plot(T, Y(:,5), 'LineWidth >> plot(T, Y(:,5), 'LineWidth Infected, {\it k}_4=0.1','Latent, {\it k}_4=0.1','Recovered, {\it k}_4=0.1', 'Infected >> legend boxoff >> ylim >> grid on >> xlabel Relative population/1000') >> set(gca