A mathematical model for the dynamics of malaria in mosquitoes feeding on a heterogeneous host population

We describe and develop a difference equation model for the dynamics of malaria in a mosquito population feeding on, infecting and getting infected from a heterogeneous population of hosts. Using the force of infection from different classes of humans to mosquitoes as parameters, we evaluate a number of entomological parameters, indicating malaria transmission levels, which can be compared to field data. By assigning different types of vector control interventions to different classes of humans and by evaluating the corresponding levels of malaria transmission, we can compare the effectiveness of these interventions. We show a numerical example of the effects of increasing coverage of insecticide-treated bed nets in a human population where the predominant malaria vector is Anopheles gambiae.

[1]  C. Garrett-Jones,et al.  THE ASSESSMENT OF INSECTICIDAL IMPACT ON THE MALARIA MOSQUITO'S VECTORIAL CAPACITY, FROM DATA ON THE PROPORTION OF PAROUS FEMALES. , 1964, Bulletin of the World Health Organization.

[2]  Nicolas Bacaer,et al.  A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. , 2005, Mathematical biosciences and engineering : MBE.

[3]  G. D. Paterson,et al.  THE ANALYSIS OF MORTALITY AND SURVIVAL RATES IN WILD POPULATION OF MOSQUITOES , 1981 .

[4]  H M Yang,et al.  Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector). , 2000, Revista de saude publica.

[5]  A. Saul,et al.  Zooprophylaxis or zoopotentiation: the outcome of introducing animals on vector transmission is highly dependent on the mosquito mortality while searching , 2003, Malaria Journal.

[6]  Antoine Flahault,et al.  An elaborated feeding cycle model for reductions in vectorial capacity of night-biting mosquitoes by insecticide-treated nets , 2007, Malaria Journal.

[7]  J. Koella,et al.  A Model for the Coevolution of Immunity and Immune Evasion in Vector‐Borne Diseases with Implications for the Epidemiology of Malaria , 2003, The American Naturalist.

[8]  R. May,et al.  The population dynamics of malaria , 1982 .

[9]  David L Smith,et al.  Statics and dynamics of malaria infection in Anopheles mosquitoes , 2004, Malaria Journal.

[10]  Gerry F. Killeen,et al.  Exploring the contributions of bed nets, cattle, insecticides and excitorepellency to malaria control: a deterministic model of mosquito host-seeking behaviour and mortality , 2007, Transactions of the Royal Society of Tropical Medicine and Hygiene.

[11]  Jia Li,et al.  Dynamic malaria models with environmental changes , 2002, Proceedings of the Thirty-Fourth Southeastern Symposium on System Theory (Cat. No.02EX540).

[12]  Amanda Ross,et al.  Mathematical modeling of the impact of malaria vaccines on the clinical epidemiology and natural history of Plasmodium falciparum malaria: Overview. , 2006, The American journal of tropical medicine and hygiene.

[13]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[14]  M E Halloran,et al.  Modeling malaria vaccines. I: New uses for old ideas. , 1989, Mathematical biosciences.

[15]  J. Botella de Maglia,et al.  [Prevention of malaria]. , 1999, Revista clinica espanola.

[16]  C. Garrett-Jones,et al.  Prognosis for Interruption of Malaria Transmission Through Assessment of the Mosquito's Vectorial Capacity , 1964, Nature.

[17]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[18]  S. Lal,et al.  Epidemiology and control of malaria , 1999, Indian journal of pediatrics.

[19]  Roy M. Anderson,et al.  The Population Dynamics of Infectious Diseases: Theory and Applications , 1982, Population and Community Biology.

[20]  G. Killeen,et al.  Rationalizing historical successes of malaria control in Africa in terms of mosquito resource availability management. , 2004, The American journal of tropical medicine and hygiene.

[21]  K Dietz,et al.  A malaria model tested in the African savannah. , 1974, Bulletin of the World Health Organization.

[22]  M. Service,et al.  Mosquito Ecology , 1993, Springer Netherlands.

[23]  Thomas A. Smith,et al.  Infectiousness of malaria-endemic human populations to vectors. , 2006, The American journal of tropical medicine and hygiene.

[24]  John B. Silver,et al.  Mosquito Ecology: Field Sampling Methods , 2008 .

[25]  Joan L. Aron,et al.  Mathematical modeling of immunity to malaria , 1989 .

[26]  B. Kay,et al.  A cyclical feeding model for pathogen transmission and its application to determine vectorial capacity from vector infection rates. , 1990 .

[27]  G. A. Ngwa,et al.  A mathematical model for endemic malaria with variable human and mosquito populations , 2000 .

[28]  B. Knols,et al.  Plasmodium falciparum sporozoites increase feeding-associated mortality of their mosquito hosts Anopheles gambiae s.l. , 2000, Parasitology.

[29]  NAKUL CHITNIS,et al.  Bifurcation Analysis of a Mathematical Model for Malaria Transmission , 2006, SIAM J. Appl. Math..

[30]  M. Kolczak,et al.  Implications of the western Kenya permethrin-treated bed net study for policy, program implementation, and future research. , 2003, The American journal of tropical medicine and hygiene.

[31]  Joan L. Aron,et al.  Mathematical modelling of immunity to malaria , 1988 .

[32]  Chris J Drakeley,et al.  Quantifying behavioural interactions between humans and mosquitoes: Evaluating the protective efficacy of insecticidal nets against malaria transmission in rural Tanzania , 2006, BMC infectious diseases.

[33]  M. Bangs,et al.  A probability model of vector behavior: effects of DDT repellency, irritancy, and toxicity in malaria control. , 2000, Journal of vector ecology : journal of the Society for Vector Ecology.

[34]  C. Lengeler,et al.  Insecticide-treated bed nets and curtains for preventing malaria. , 2004, The Cochrane database of systematic reviews.